https://cs1230.graphics/assets/pages/labs/lab3.page.1f66a4cd.js

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2`,`
3`,e.exports.jsx(s.h1,{id:"lab-3-transforms-and-parsing",children:e.exports.jsx(s.a,{href:"#lab-3-transforms-and-parsing",children:"Lab 3: Transforms and Parsing"})}),`
4`,e.exports.jsx(s.p,{children:e.exports.jsx(s.a,{href:"https://gh-invites.cs.brown.edu/i/CPzXAdzR",target:"_blank",rel:"noopener noreferrer",children:"Assignment invite link"})}),`
5`,e.exports.jsx(s.div,{className:"task-no-number-callout callout",children:e.exports.jsxs(s.p,{children:["Please put your answers to written questions in this lab, if any, in a Markdown file named ",e.exports.jsx(s.co

5de,{children:"README.md"})," in your lab repo."]})}),`
6`,e.exports.jsx(s.h2,{id:"introduction",children:e.exports.jsx(s.a,{href:"#introduction",children:"Introduction"})}),`
7`,e.exports.jsxs(s.p,{children:["Welcome to lab 3! The goal of this lab is to help you get more comfortable with ",e.exports.jsx(s.strong,{children:"2D & 3D transformations"}),", ",e.exports.jsx(s.strong,{children:"coordinate spaces"}),", and ",e.exports.jsx(s.strong,{children:"scene graphs"}),"."]}),`
8`,e.exports.jsx(s.p,{children:"By the end of this lab, you will be able to build transformation matrices, combine them correctly, and then use those ideas while traversing a scene graph to produce renderable data."}),`
9`,e.exports.jsx(s.h3,{id:"objectives",children:e.exports.jsx(s.a,{href:"#objectives",children:"Objectives"})}),`
10`,e.exports.jsx(s.div,{className:"warning-callout callout",children:e.exports.jsx(s.p,{children:"This lab involves more conceptual understanding than previous ones. Be sure to take your time reading through the sections, and don't be afraid to ask questions if you're confused!"})}),`
11`,e.exports.jsxs(s.ol,{children:[`
12`,e.exports.jsxs(s.li,{children:["Learn how matrices are used to represent ",e.exports.jsx(s.strong,{children:"scaling"}),", ",e.exports.jsx(s.strong,{children:"rotation"}),", and ",e.exports.jsx(s.strong,{children:"translation"})," transformations"]}),`
13`,e.exports.jsxs(s.li,{children:["Understand how to ",e.exports.jsx(s.strong,{children:"compose"})," multiple transformations to obtain a ",e.exports.jsx(s.strong,{children:"cumulative transformation matrix"})]}),`
14`,e.exports.jsxs(s.li,{children:["Reason about ",e.exports.jsx(s.strong,{children:"world"}),", ",e.exports.jsx(s.strong,{children:"object"}),", ",e.exports.jsx(s.strong,{children:"camera"}),", and ",e.exports.jsx(s.strong,{children:"local"})," coordinate spaces"]}),`
15`,e.exports.jsxs(s.li,{children:["Traverse a scene graph as ",e.exports.jsx(s.code,{children:"SceneData"})]}),`
16`,e.exports.jsxs(s.li,{children:["Convert ",e.exports.jsx(s.code,{children:"SceneData"})," into ",e.exports.jsx(s.code,{children:"RenderData"})," for rendering"]}),`
17`]}),`
18`,e.exports.jsx(s.h2,{id:"building-transformations",children:e.exports.jsx(s.a,{href:"#building-transformations",children:"Building Transformations"})}),`
19`,e.exports.jsx(s.h3,{id:"representing-transformations-as-matrices",children:e.exports.jsx(s.a,{href:"#representing-transformations-as-matrices",children:"Representing Transformations as Matrices"})}),`
20`,e.exports.jsx(s.p,{children:"A transformation can be thought of as a function."}),`
21`,e.exports.jsx(t,{images:[{src:"/labs/lab3/transformIntro.png",alt:"A transformation takes in an input vector and returns a transformed output vector."}],figNumber:1,figCaption:"A transformation takes in an input vector and returns a transformed output vector."}),`
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51`,e.exports.jsxs(s.p,{children:["In ",e.exports.jsx(s.strong,{children:"3D"}),", this is a bit more complex. Rather than always rotating CCW about the origin, 3D allows for rotation around any arbitrary ",e.exports.jsx(s.strong,{children:"axis"}),"."]}),`
52`,e.exports.jsxs(s.p,{children:["There are many ways to describe rotations in 3D (as covered during the lectures), but we'll use the axis-aligned ",e.exports.jsx(s.strong,{children:"Euler angles"})," approach as this is the simplest for when we construct our own matrices."]}),`
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64`,e.exports.jsx(s.h3,{id:"translation-and-homogeneous-coordinates",children:e.exports.jsx(s.a,{href:"#translation-and-homogeneous-coordinates",children:"Translation and Homogeneous Coordinates"})}),`
65`,e.exports.jsxs(s.p,{children:[e.exports.jsx(s.strong,{children:"Translation"})," moves a point without changing its shape or orientation. Unlike scaling and rotation, translation is not linear, it is an ",e.exports.jsx(s.strong,{children:e.exports.jsx(s.a,{href:"https://en.wikipedia.org/wiki/Affine_transformation",target:"_blank",rel:"noopener noreferrer",children:"affine transformation"})}),"."]}),`
66`,e.exports.jsx(s.p,{children:"Generally speaking, linear transformations are a strict subset of affine transformations."}),`
67`,e.exports.jsx(t,{images:[{src:"/labs/lab3/transformTypes.png",alt:"Simple venn diagram showing that linear transformations are a strict subset of affine transformations."}],targetWidth:"50%",figNumber:4,figCaption:"Linear transformations are a strict subset of affine transformations."}),`
68`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Extra: more information about transformation classification"}),e.exports.jsxs(s.p,{children:["There are many ways to classify transformations. In the paragraphs above, we are considering their ",e.exports.jsx(s.strong,{children:"mathematical"})," formulation: translation is not a linear transformation as it does not preserve the origin, and this conclusion is entirely based on the definition of what a ",e.exports.jsx(s.em,{children:"linear"})," transformation is."]}),e.exports.jsxs(s.blockquote,{children:[`
69`,e.exports.jsx(s.p,{children:e.exports.jsx(s.em,{children:"You will soon see that what is non-linear in one dimension, can actually be linear in a higher dimension \u{1F609}."})}),`
70`]}),e.exports.jsxs(s.p,{children:["There is, of course, another way to look at classify transformations. We might do so based on what geometric features they ",e.exports.jsx(s.em,{children:"preserve"}),":"]}),e.exports.jsxs(s.blockquote,{children:[`
71`,e.exports.jsxs(s.table,{children:[e.exports.jsx(s.thead,{children:e.exports.jsxs(s.tr,{children:[e.exports.jsx(s.th,{align:"left",children:"Type Of Transformation"}),e.exports.jsx(s.th,{align:"left",children:"What They Preserve"}),e.exports.jsx(s.th,{align:"left",children:"Examples"})]})}),e.exports.jsxs(s.tbody,{children:[e.exports.jsxs(s.tr,{children:[e.exports.jsx(s.td,{align:"left",children:"Displacements"}),e.exports.jsxs(s.td,{align:"left",children:["Distances and ",e.exports.jsx(s.em,{children:"oriented"})," angles"]}),e.exports.jsx(s.td,{align:"left",children:"Translations"})]}),e.exports.jsxs(s.tr,{children:[e.exports.jsx(s.td,{align:"left",children:"Isometries"}),e.exports.jsx(s.td,{align:"left",children:"Distances and angles"}),e.exports.jsx(s.td,{align:"left",children:"Rotations, reflections, and the above"})]}),e.exports.jsxs(s.tr,{children:[e.exports.jsx(s.td,{align:"left",children:"Similarities"}),e.exports.jsx(s.td,{align:"left",children:"Ratios between distances and angles"}),e.exports.jsx(s.td,{align:"left",children:"Uniform scaling, and the above"})]}),e.exports.jsxs(s.tr,{children:[e.exports.jsx(s.td,{align:"left",children:"Affine transformations"}),e.exports.jsx(s.td,{align:"left",children:"Parallelism"}),e.exports.jsx(s.td,{align:"left",children:"Non-uniform scaling, shear, and the above"})]}),e.exports.jsxs(s.tr,{children:[e.exports.jsx(s.td,{align:"left",children:"Projective transformations"}),e.exports.jsx(s.td,{align:"left",children:"Collinearity"}),e.exports.jsx(s.td,{align:"left",children:"Perspective projection, and the above"})]})]})]}),`
72`,e.exports.jsx(s.p,{children:e.exports.jsxs(s.em,{children:["Adapted from the Wikipedia page on ",e.exports.jsx(s.a,{href:"https://en.wikipedia.org/wiki/Geometric_transformation",target:"_blank",rel:"noopener noreferrer",children:"geometric transformations"})]})}),`
73`]})]}),`
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-0.5)",children:e.exports.jsx(s.use,{"data-c":"5D",xlinkHref:"#MJX-50-TEX-S3-5D"})})]}),e.exports.jsx(s.g,{"data-mml-node":"mo",transform:"translate(13565,0)",children:e.exports.jsx(s.use,{"data-c":"2260",xlinkHref:"#MJX-50-TEX-N-2260"})}),e.exports.jsx(s.g,{"data-mml-node":"TeXAtom","data-mjx-texclass":"ORD",transform:"translate(14620.8,0)",children:e.exports.jsx(s.g,{"data-mml-node":"mi",children:e.exports.jsx(s.use,{"data-c":"1D42D",xlinkHref:"#MJX-50-TEX-B-1D42D"})})})]})})]})})}),e.exports.jsxs(s.p,{children:["Oh dear. No matter what values we put in ",e.exports.jsx(s.co

74de,{children:"2x2"})," matrix, the output can never be equal to non-zero vector ",e.exports.jsx(s.span,{className:"math math-inline",children:e.exports.jsx(s["mjx-container"],{className:"MathJax",jax:"SVG",children:e.exports.jsxs(s.svg,{style:{verticalAlign:"-0.011ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.011ex",height:"1.448ex",role:"img",focusable:"false",viewBox:"0 -635 447 640",xmlnsXlink:"http://www.w3.org/1999/xlink",children:[e.exports.jsx(s.defs,{children:e.exports.jsx(s.path,{id:"MJX-51-TEX-B-1D42D",d:"M272 49Q320 49 320 136V145V177H382V143Q382 106 380 99Q374 62 349 36T285 -2L272 -5H247Q173 -5 134 27Q109 46 102 74T94 160Q94 171 94 199T95 245V382H21V433H25Q58 433 90 456Q121 479 140 523T162 621V635H224V444H363V382H224V239V207V149Q224 98 228 81T249 55Q261 49 272 49Z"})}),e.exports.jsx(s.g,{stroke:"currentColor",fill:"currentColor",strokeWidth:"0",transform:"scale(1,-1)",children:e.exports.jsx(s.g,{"data-mml-node":"math",children:e.exports.jsx(s.g,{"data-mml-node":"TeXAtom","data-mjx-texclass":"ORD",children:e.exports.jsx(s.g,{"data-mml-node":"mi",children:e.exports.jsx(s.use,{"data-c":"1D42D",xlinkHref:"#MJX-51-TEX-B-1D42D"})})})})})]})})}),". Clearly, a ",e.exports.jsx(s.code,{children:"2x2"})," matrix is not sufficient for representing a translation of a ",e.exports.jsx(s.code,{children:"2x1"})," point in this way (and the same can be shown for ",e.exports.jsx(s.code,{children:"3x3"})," matrices, with ",e.exports.jsx(s.code,{children:"3x1"})," points)."]})]}),`
75`,e.exports.jsxs(s.p,{children:["If we wish to represent translations as matrices, we must now introduce ",e.exports.jsx(s.strong,{children:"homogeneous coordinates"}),"."]}),`
76`,e.exports.jsx(s.h4,{id:"homogeneous-coordinates",children:e.exports.jsx(s.a,{href:"#homogeneous-coordinates",children:"Homogeneous Coordinates"})}),`
77`,e.exports.jsxs(s.p,{children:["While homogeneous coordinates are pretty simple to ",e.exports.jsx(s.em,{children:"use"}),", they might be somewhat challenging to understand. The idea is this: take any existing point or vector, and ",e.exports.jsx(s.strong,{children:"just add another dimension to it"}),". Then, do the same for transformation matrices."]}),`
78`,e.exports.jsxs(s.p,{children:["In 3D, for example, this turns a ",e.exports.jsx(s.code,{children:"3x1"})," point into a ",e.exports.jsx(s.code,{children:"4x1"})," point. We typically refer to this new, fourth dimension as ",e.exports.jsx(s.span,{className:"math math-inline",children:e.exports.jsx(s["mjx-container"],{className:"MathJax",jax:"SVG",children:e.exports.jsxs(s.svg,{style:{verticalAlign:"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.62ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 716 454",xmlnsXlink:"http://www.w3.org/1999/xlink",children:[e.exports.jsx(s.defs,{children:e.exports.jsx(s.path,{id:"MJX-52-TEX-I-1D464",d:"M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"})}),e.exports.jsx(s.g,{stroke:"currentColor",fill:"currentColor",strokeWidth:"0",transform:"scale(1,-1)",children:e.exports.jsx(s.g,{"data-mml-node":"math",children:e.exports.jsx(s.g,{"data-mml-node":"mi",children:e.exports.jsx(s.use,{"data-c":"1D464",xlinkHref:"#MJX-52-TEX-I-1D464"})})})})]})})}),". But what should we set this ",e.exports.jsx(s.span,{className:"math math-inline",children:e.exports.jsx(s["mjx-container"],{className:"MathJax",jax:"SVG",children:e.exports.jsxs(s.svg,{style:{verticalAlign:"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.62ex",height:"1.027ex",role:"img",focu

78sable:"false",viewBox:"0 -443 716 454",xmlnsXlink:"http://www.w3.org/1999/xlink",children:[e.exports.jsx(s.defs,{children:e.exports.jsx(s.path,{id:"MJX-53-TEX-I-1D464",d:"M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"})}),e.exports.jsx(s.g,{stroke:"currentColor",fill:"currentColor",strokeWidth:"0",transform:"scale(1,-1)",children:e.exports.jsx(s.g,{"data-mml-node":"math",children:e.exports.jsx(s.g,{"data-mml-node":"mi",children:e.exports.jsx(s.use,{"data-c":"1D464",xlinkHref:"#MJX-53-TEX-I-1D464"})})})})]})})})," value to?"]}),`
79`,e.exports.jsxs(s.div,{className:"success-callout callout",children:[e.exports.jsx(s.p,{children:e.exports.jsxs(s.strong,{children:["For points (position vectors), we set ",e.exports.jsx(s.span,{className:"math math-inline",children:e.exports.jsx(s["mjx-container"],{className:"MathJax",jax:"SVG",children:e.exports.jsxs(s.svg,{style:{verticalAlign:"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.768ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2549.6 748",xmlnsXlink:"http://www.w3.org/1999/xlink",children:[e.exports.jsxs(s.defs,{children:[e.exports.jsx(s.path,{id:"MJX-54-TEX-I-1D464",d:"M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"}),e.exports.jsx(s.path,{id:"MJX-54-TEX-N-3D",d:"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"}),e.exports.jsx(s.path,{id:"MJX-54-TEX-N-31",d:"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"})]}),e.exports.jsx(s.g,{stroke:"currentColor",fill:"currentColor",strokeWidth:"0",transform:"scale(1,-1)",children:e.exports.jsxs(s.g,{"data-mml-node":"math",children:[e.exports.jsx(s.g,{"data-mml-node":"mi",children:e.exports.jsx(s.use,{"data-c":"1D464",xlinkHref:"#MJX-54-TEX-I-1D464"})}),e.exports.jsx(s.g,{"data-mml-node":"mo",transform:"translate(993.8,0)",children:e.exports.jsx(s.use,{"data-c":"3D",xlinkHref:"#MJX-54-TEX-N-3D"})}),e.exports.jsx(s.g,{"data-mml-node":"mn",transform:"translate(2049.6,0)",children:e.exports.jsx(s.use,{"data-c":"31",xlinkHref:"#MJX-54-TEX-N-31"})})]})})]})})}),"; and for vectors, we set ",e.exports.jsx(s.span,{className:"math math-inline",children:e.exports.jsx(s["mjx-container"],{className:"MathJax",jax:"SVG",children:e.exports.jsxs(s.svg,{style:{verticalAlign:"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.768ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2549.6 748",xmlnsXlink:"http://www.w3.org/1999/xlink",children:[e.exports.jsxs(s.defs,{children:[e.exports.jsx(s.path,{id:"MJX-55-TEX-I-1D464",d:"M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q2

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94`,e.exports.jsxs(s.p,{children:["Now that we know how to perform translation in ",e.exports.jsx(s.co

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95`,e.exports.jsx(t,{images:[{src:"/labs/lab3/vectorTranslation.png",alt:"TODO"}],targetWidth:"75%",figNumber:5,figCaption:'Translating two points (before: red; after: blue). Observe that the difference between them, the black arrow, remains the same; if we were to attempt to "translate" the vector, it would remain unchanged.'}),`
96`,e.exports.jsx(s.div,{className:"task-callout callout",children:e.exports.jsxs(s.p,{children:["Fill in ",e.exports.jsx(s.code,{children:"getTranslationMatrix()"})," so that it returns the ",e.exports.jsx(s.code,{children:"4x4"})," transformation matrix (as a ",e.exports.jsx(s.code,{children:"glm::mat4"}),") that translates along each axis by the given coordinates."]})}),`
97`,e.exports.jsx(s.div,{className:"task-callout callout",children:e.exports.jsxs(s.p,{children:["Then update ",e.exports.jsx(s.code,{children:"getScalingMatrix()"}),", ",e.exports.jsx(s.code,{children:"getRotationMatrixX()"}),", ",e.exports.jsx(s.code,{children:"getRotationMatrixY()"}),", and ",e.exports.jsx(s.code,{children:"getRotationMatrixZ()"})," to work with homogeneous coordinates so they return ",e.exports.jsx(s.code,{children:"glm::mat4"}),"s instead of ",e.exports.jsx(s.code,{children:"glm::mat3"}),"s. Do not forget to update the headers in ",e.exports.jsx(s.code,{children:"transforms.h"}),"."]})}),`
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99`,e.exports.jsxs(s.p,{children:["Being able to apply only a single transformation would probably make it hard to create interesting scenes unless your goal is to make a brick wall. We can apply multiple transformations by composing them. Mathematically, this is represented by multiplying the respective matrices ",e.exports.jsx(s.strong,{children:"in the order that the transformations are applied"}),"."]}),`
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104`,e.exports.jsxs(s.blockquote,{children:[`
105`,e.exports.jsxs(s.p,{children:[e.exports.jsx(s.strong,{children:"Important"}),": Matrix multiplication is ",e.exports.jsx(s.strong,{children:"not commutative"}

105),", so changing the order changes the result."]}),`
106`]}),`
107`,e.exports.jsx(s.h3,{id:"ordering-scale-rotation-and-translation",children:e.exports.jsx(s.a,{href:"#ordering-scale-rotation-and-translation",children:"Ordering (S)cale, (R)otation, and (T)ranslation"})}),`
108`,e.exports.jsx(s.p,{children:"If you have one object that you want to apply multiple individual scale, rotation, and translation transformations to, you should be careful of the order in which you compose the transformations. Usually, you want to use a standardized order in which you apply transformations to maintain consistency."}),`
109`,e.exports.jsxs(s.p,{children:["One widely used ordering is ",e.exports.jsx(s.strong,{children:"TRS"}),". This means that scaling is first, then rotation, then translation."]}),`
110`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Why TRS ordering works"}),e.exports.jsx(s.p,{children:"Let's say we have a square at the origin that we want to perform the following transformations on:"}),e.exports.jsxs(s.ul,{children:[`
111`,e.exports.jsx(s.li,{children:"Scale x by 1.5 and y by 2"}),`
112`,e.exports.jsx(s.li,{children:"Rotate by 45\xB0"}),`
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116`,e.exports.jsx(s.p,{children:"Now that you know how to build and compose transforms, we can use them on a scene graph."}),`
117`,e.exports.jsx(t,{images:[{src:"/labs/lab3/transformGraph.png",alt:"Scene graph"}],figNumber:8,figCaption:"Scene graph"}),`
118`,e.exports.jsx(s.p,{children:"There are a lot of different parts of this graph to understand, but for now let's focus on some of the labeled transformations. A, B, C, and D all denote individual transformation matrices that involve some combination of scaling, rotating, and translating."}),`
119`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"How to read the transformations"}),e.exports.jsx(s.p,{children:"At the top of the graph is the world origin. From it, the rest of the objects and camera branch off, with nodes in between to represent the transformations applied to the objects and camera."}),e.exports.jsx(s.p,{children:"Here's a guide to our notation of transformations:"}),e.exports.jsx(s.pre,{children:e.exports.jsxs(s.code,{className:"code-highlight",children:[e.exports.jsx(s.span,{className:"code-line",children:`S X,Y,Z:   scale by factors X, Y, and Z along the corresponding axes
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121`}),e.exports.jsx(s.span,{className:"code-line",children:`T X,Y,Z:   translate by X, Y, and Z along the corresponding axes
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123`,e.exports.jsx(s.div,{className:"task-callout callout",children:e.exports.jsxs(s.p,{children:["Fill in functions ",e.exports.jsx(s.co

123de,{children:"getMatrixA"}),", ",e.exports.jsx(s.code,{children:"getMatrixB"}),", ",e.exports.jsx(s.code,{children:"getMatrixC"}),", and ",e.exports.jsx(s.code,{children:"getMatrixD"})," using the functions you defined in Tasks 1-4 to return the matrices corresponding to the transformations described in the graph."]})}),`
124`,e.exports.jsx(s.p,{children:"In a scene graph, a node's transforms apply to everything below it. To find the final transform for an object, multiply the transforms along the path from the root to the node that contains that object."}),`
125`,e.exports.jsxs(s.p,{children:["That final product is the object's cumulative transformation matrix, or ",e.exports.jsx(s.strong,{children:"CTM"}),"."]}),`
126`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"How to think about the traversal"}),e.exports.jsxs(s.p,{children:["Looking at our graph again, each leaf of the tree is an object in the scene. Traversing the tree from the object to the root will create a path through all of the transformations applied to that object in the scene. So to transform Object 1 to world space, for example, first apply transformation A then C. The cumulative transformation matrix of an object in the scene, resulting from this ordered multiplication of matrices, is referred to as the object's ",e.exports.jsx(s.strong,{children:"model matrix"}),"."]}),e.exports.jsx(s.p,{children:"Previously, we emphasized the need to order each of the T, R, and S transformations. Now we may be dealing with multiple matrices composed of multiple T, R, and S transformations, but for the higher level ordering we follow the graph hierarchy."})]}),`
127`,e.exports.jsx(s.h3,{id:"demo-and-inverse-rotation",children:e.exports.jsx(s.a,{href:"#demo-and-inverse-rotation",children:"Demo And Inverse Rotation"})}),`
128`,e.exports.jsx(s.p,{children:"To help you check your work, the stencil includes a visualizer that lets you apply the transformation matrices from the graph."}),`
129`,e.exports.jsx(t,{images:[{src:"/labs/lab3/demo.png",alt:"How the program should look when you initially run it."}],figNumber:9,figCaption:"How the program should look when you initially run it."}),`
130`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"How to use the demo"}),e.exports.jsx(s.p,{children:"You can click and drag to move around and scroll to zoom."}),e.exports.jsx(s.p,{children:"The white grid in the background represents the world coordinate system. The white axes at the origin represent your current coordinate system. Though they aren't labeled in the demo, these are labeled here for your reference."}),e.exports.jsx(s.p,{children:`Each of the buttons A, B, C, and D are linked to the functions you completed in the last task to return transformation matrices. Pressing any of these buttons will apply the corresponding function's transformation to the white axes. We have also provided you with inverse buttons for each of these that will return the inverse of the corresponding matrix. (Don't worry about the "View" or "Rotation" buttons for now, you'll be implementing those later.)`}),e.exports.jsx(s.p,{children:'As you press the buttons, the text underneath that says "you" will update to reflect the order of transformations you use. Pressing the "reset" button will move your axes back to the origin and reset this label.'})]}),`
131`,e.exports.jsx(s.div,{className:"error-callout callout",children:e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Having issues running your code?"}),e.exports.jsx(s.p,{children:"If you run your code and don't see the axes, or if your program immediately crashes with an error along the lines of"}),e.exports.jsxs(s.p,{children:[e.exports.jsx(s.code,{children:"terminating with uncaught exception of type std::runtime_error: Failed to open shader: resources/shaders/grid.vert"}),`
132this is for you!`]}),e.exports.jsx(s.p,{children:"On the left side of Qt Creator go to the Projects > Run menu and check your working directory. Ensure that the listed filepath is the absolute path to the root folder of the lab git repo. The most likely issue is that the program is unable to load the shader files we use for rendering the scene because the filepaths are relative to the root directory!"}),e.exports.jsx(t,{images:[{src:"/labs/lab3/workingDirWrong.jpg",alt:"TODO"}],figNumber:10,figCaption:"Incorrect filepath"}),e.exports.jsx(s.p,{children:"Correct:"}),e.exports.jsx(t,{images:[{src:"/labs/lab3/workingDirRight.jpg",alt:"TODO"}],figNumber:11,figCaption:"Correct absolute filepath to lab folder"})]})}),`
133`,e.exports.jsxs(s.p,{children:["There are colored sets of axes throughout which represent the coordinate systems of the different objects in the scene as described 

133in the graph. These are not labeled because ",e.exports.jsx(s.strong,{children:"it will be up to you to figure out which belongs to which object."})]}),`
134`,e.exports.jsx(t,{images:[{src:"/labs/lab3/transformGraph.png",alt:"Scene graph"}],figNumber:12,figCaption:"Scene graph"}),`
135`,e.exports.jsxs(s.div,{className:"task-callout callout",children:[e.exports.jsx(s.p,{children:"Use the A, B, C, and D buttons to transform the white axes from the world origin to the coordinate system of each object represented by the colored axes. Your task is to find the transformations for Objects 1, 2, and 3 given in the scene graph and find which colored axes correspond to each object."}),e.exports.jsxs(s.blockquote,{children:[`
136`,e.exports.jsxs(s.p,{children:[e.exports.jsx(s.strong,{children:"Note:"})," You will only end up matching 3 of the 4 colored axes. The fourth is for a later task."]}),`
137`]}),e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Hint"}),e.exports.jsx(s.p,{children:"You can think of the white axes as starting in each object's object space, and your goal is to follow the transformation graph to transform it into world space."}),e.exports.jsx(s.p,{children:"If you have implemented your matrices correctly and apply them in the correct order as described in the provided transformation graph, you should see the white axes line up with another colored axes."}),e.exports.jsxs("b",{children:[" ",e.exports.jsxs(s.p,{children:["Note: Each colored axes is an ",e.exports.jsx("u",{children:"object"}),` from the transformation graph. This means it may or may not require
138multiple transformations to reach it. Using the transformations you created, you should be able to match 3 of
139the 4 colored axes. We recommend rereading the paragraphs above this task if you are confused.`," "]})]})]})]}),`
140`,e.exports.jsxs(s.p,{children:["As a quick debugging exercise, the stencil also includes an inverse rotation function called ",e.exports.jsx(s.code,{children:"getInverseRotation()"}),". The function relies on the useful fact that the inverse of a rotation matrix is its transpose. However, it currently has a bug \u{1F41B}"]}),`
141`,e.exports.jsxs(s.div,{className:"task-callout callout",children:[e.exports.jsxs(s.ol,{children:[`
142`,e.exports.jsxs(s.li,{children:["Press the ",e.exports.jsx(s.code,{children:"Rotation"})," button in the visualizer.",`
143`,e.exports.jsxs(s.ul,{children:[`
144`,e.exports.jsx(s.li,{children:"This function is already implemented and rotates your coordinate space about the vertical axis by a small angle."}),`
145`]}),`
146`]}),`
147`,e.exports.jsxs(s.li,{children:["Press the ",e.exports.jsx(s.code,{children:"Rotation^-1"})," button (which calls",e.exports.jsx(s.code,{children:"getInverseRotation"}),"). Does it apply the transformation you expect it to?"]}),`
148`,e.exports.jsxs(s.li,{children:["Identify and fix the bug in ",e.exports.jsx(s.code,{children:"getInverseRotation()"}),"."]}),`
149`]}),e.exports.jsxs(s.blockquote,{children:[`
150`,e.exports.jsxs(s.p,{children:[e.exports.jsx(s.strong,{children:"Note:"})," You may not use ",e.exports.jsx(s.code,{children:"glm::inverse"})," or ",e.exports.jsx(s.code,{children:"glm::transpose"})," to implement this function."]}),`
151`]}),e.exports.jsxs(s.p,{children:["Verify that ",e.exports.jsx(s.code,{children:"Rotation"})," followed by ",e.exports.jsx(s.code,{children:"Rotation^-1"})," returns the axes to their original state."]})]}),`
152`,e.exports.jsx(s.h3,{id:"camera-view-matrix",children:e.exports.jsx(s.a,{href:"#camera-view-matrix",children:"Camera View Matrix"})}),`
153`,e.exports.jsxs(s.p,{children:["The camera's placement in world space is described by a position and orientation. A key part of rendering is showing the scene from the camera's point of view. To do so we use the inverse of the camera transform. That inverse is the ",e.exports.jsx(s.strong,{children:"view matrix"}),". By applying the view matrix to all points in the scene, we transform them from world space into camera space, and thus the camera's point of view."]}),`
154`,e.exports.jsx(t,{images:[{src:"/labs/lab3/viewTransform.png",alt:"Transformation from world space to camera space using the view matrix"}],figNumber:13,figCaption:"Transformation from world space to camera space using the view matrix"}),`
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156`,e.exports.jsx(t,{images:[{src:"/labs/lab3/cameraAxes.png",alt:"Camera axes"}],figNumber:14,figCaption:"Camera look and up vectors, uvw axes"}),`
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166`,e.exports.jsx(t,{images:[{src:"/labs/lab3/transformGraph.png",alt:"Transformation graph"}],figNumber:15,figCaption:"Transformation graph"}),`
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168`,e.exports.jsx(s.h2,{id:"coordinate-spaces",children:e.exports.jsx(s.a,{href:"#coordinate-spaces",children:"Coordinate Spaces"})}),`
169`,e.exports.jsxs(s.p,{children:["In discussing transformations, we've mentioned the idea of transforming between ",e.exports.jsx(s.strong,{children:"coordinate spaces"}),", but what are coordinate spaces? This is an important concept as you work on building your raytracer. You will often find that certain calculations make sense when you work with them in specific coordinate spaces, but when you're dealing with points and vectors in different spaces you need to know how to use transformations to move between them."]}),`
170`,e.exports.jsxs(s.p,{children:["In this lab, we use three coordinate spaces often: ",e.exports.jsx(s.strong,{children:"world space"}),", ",e.exports.jsx(s.strong,{children:"camera space"}),", and ",e.exports.jsx(s.strong,{children:"object space"}),"."]}),`
171`,e.exports.jsxs(s.ol,{children:[`
172`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.strong,{children:"World space"})," is the global coordinate system for the scene."]}),`
173`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.strong,{children:"Camera space"})," is the coordinate system defined by the camera."]}),`
174`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.strong,{children:"Object space"})," is the local coordinate system in which a single object is defined."]}),`
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176),e.exports.jsx(s.g,{stroke:"currentColor",fill:"currentColor",strokeWidth:"0",transform:"scale(1,-1)",children:e.exports.jsxs(s.g,{"data-mml-node":"math",children:[e.exports.jsx(s.g,{"data-mml-node":"mi",children:e.exports.jsx(s.use,{"data-c":"1D465",xlinkHref:"#MJX-103-TEX-I-1D465"})}),e.exports.jsx(s.g,{"data-mml-node":"mi",transform:"translate(572,0)",children:e.exports.jsx(s.use,{"data-c":"1D466",xlinkHref:"#MJX-103-TEX-I-1D466"})}),e.exports.jsx(s.g,{"data-mml-node":"mi",transform:"translate(1062,0)",children:e.exports.jsx(s.use,{"data-c":"1D467",xlinkHref:"#MJX-103-TEX-I-1D467"})})]})})]})})}),". In part 2, we went over how to get the view matrix, which takes world space points and transforms them into camera space."]}),e.exports.jsx(s.p,{children:e.exports.jsx(s.strong,{children:"Object Space"})}),e.exports.jsx(s.p,{children:"Object space is pretty much what it sounds like - the coordinate system in which an object is defined. In the demo, these are represented by the little sets of axes drawn for each object in the scene."})]}),`
177`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Why do we need coordinates specific to each object?"}),e.exports.jsx(s.p,{children:"For example, you might want to make a bunch of variations of a sphere that are all different sizes and in different locations. Rather than define each sphere separately, we can define a single sphere as a set of points around an origin, and then transform those points. You can perform calculations on points in the sphere relative to its own central origin, and then use its model matrix to get those points in world space."})]}),`
178`,e.exports.jsx(s.h3,{id:"relating-all-three",children:e.exports.jsx(s.a,{href:"#relating-all-three",children:"Relating All Three"})}),`
179`,e.exports.jsx(s.p,{children:"Here's a simpler graphic that helps to sum up the relationships between everything we covered so far in this lab."}),`
180`,e.exports.jsx(t,{images:[{src:"/labs/lab3/spaces.png",alt:"Coordinate spaces"}],figNumber:16,figCaption:"Relating world, camera, and object space"}),`
181`,e.exports.jsx(s.p,{children:"The arrows indicate the direction of transformation that the labeled matrix provides. An object's model matrix will convert from that object's space to world space. The view matrix will convert from world space to camera space. The inverses of these matrices provide the transformation of the opposite direction."}),`
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182),e.exports.jsx(s.g,{stroke:"currentColor",fill:"currentColor",strokeWidth:"0",transform:"scale(1,-1)",children:e.exports.jsx(s.g,{"data-mml-node":"math",children:e.exports.jsx(s.g,{"data-mml-node":"mi",children:e.exports.jsx(s.use,{"data-c":"1D449",xlinkHref:"#MJX-107-TEX-I-1D449"})})})})]})})}),". Describe briefly the calculations necessary to find the distance between these two points in world space."]}),e.exports.jsx(s.p,{children:e.exports.jsx(s.em,{children:'Your response should be no more complex than just stating "multiply __ and __ to get __ in ______ space. Then..."'})})]}),`
183`,e.exports.jsx(s.h2,{id:"scene-data-and-render-data",children:e.exports.jsx(s.a,{href:"#scene-data-and-render-data",children:"Scene Data and Render Data"})}),`
184`,e.exports.jsx(s.h3,{id:"scene-data-vs-render-data",children:e.exports.jsx(s.a,{href:"#scene-data-vs-render-data",children:"Scene Data vs. Render Data"})}),`
185`,e.exports.jsx(s.p,{children:"We have spent most of this lab building and composing transformation matrices. Now we use those ideas to understand how a scene file becomes renderable data, and ultimately cool 3D scenes."}),`
186`,e.exports.jsxs(s.ol,{children:[`
187`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.code,{children:"SceneData"})," is the tree-based representation used while building a scene, known as a ",e.exports.jsx(s.a,{href:"https://en.wikipedia.org/wiki/Scene_graph",target:"_blank",rel:"noopener noreferrer",children:"scene graph"}),".",`
188`,e.exports.jsxs(s.ul,{children:[`
189`,e.exports.jsx(s.li,{children:"This is often arranged in a tree structure that groups logical (and often spatial) relationships between objects in the scene."}),`
190`]}),`
191`]}),`
192`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.code,{children:"RenderData"})," is the flattened representation used while rendering.",`
193`,e.exports.jsxs(s.ul,{children:[`
194`,e.exports.jsxs(s.li,{children:["In ",e.exports.jsx(s.code,{children:"RenderData"}),", each object/primitive stores its final cumulative transform, so the renderer no longer has to traverse the scene graph."]}),`
195`]}),`
196`]}),`
197`]}),`
198`,e.exports.jsxs(s.p,{children:["Take a look at the two figures below. In this lab, your task will be to write a parser which transforms ",e.exports.jsx(s.code,{children:"SceneData"})," to ",e.exports.jsx(s.code,{children:"RenderData"}),"."]}),`
199`,e.exports.jsx(t,{images:[{src:"/labs/lab3/scene-vs-render-1.png",alt:"TODO"}],figNumber:17,children:e.exports.jsxs(s.p,{children:["Transforming ",e.exports.jsx(s.code,{children:"SceneData"})," into ",e.exports.jsx(s.code,{children:"RenderData"}),". Conceptually, they store the same information, just in a different format!"]})}),`
200`,e.exports.jsx(t,{images:[{src:"/labs/lab3/scene-vs-render-2.png",alt:"TODO"}],figNumber:18,figCaption:"Comparing scene graphs and lists of primitives, as data structures."}),`
201`,e.exports.jsxs(s.p,{children:["In ",e.exports.jsx(s.a,{href:"#figure-17",children:"Figure 17"}),", observe how the ",e.exports.jsx(s.code,{children:"SceneGraph"})," and ",e.exports.jsx(s.code,{children:"PrimitivesList"})," are the only things that differentiate ",e.exports.jsx(s.code,{children:"SceneData"})," from ",e.exports.jsx(s.code,{children:"RenderData"}),". ",e.exports.jsx(s.a,{href:"#figure-18",children:"Figure 18"})," shows how primitives and their transformations are stored differently in these data structures."]}),`
202`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Extra: why do we use a vector/list to store primitives?"}),e.exports.jsxs(s.p,{children:["If you have started ",e.exports.jsx(s.code,{children:"Project 2: Intersect"}),", you might have reasoned that one of the reasons ray tracing is so computationally expensive is because we need to check for ray-primitive intersections. This is ",e.exports.jsx(s.em,{children:"especially"})," true when there are many primitives in the scene to check against."]}),e.exports.jsxs(s.p,{children:["We use a ",e.exports.jsx(s.strong,{children:"vector/list"})," to iterate through all the primitives in the scene because it is simple to implement, and has traditionally been sufficient for the requirements of this course."]}

202),e.exports.jsxs(s.p,{children:["That said, there isn't any reason that this part of ",e.exports.jsx(s.code,{children:"RenderData"})," ",e.exports.jsx(s.em,{children:"has"}),' to be a vector/list. If you want to get fancy, there are more efficient alternatives which allow for much faster ray-primitive intersection tests (see: "accelerated" data structures like octrees, bounding-volume hierarchies (BVHs), and KD-trees, all covered in lectures).']})]}),`
203`,e.exports.jsx(s.h3,{id:"scene-data",children:e.exports.jsx(s.a,{href:"#scene-data",children:"Scene Data"})}),`
204`,e.exports.jsxs(s.p,{children:["The parser gets the data it needs from ",e.exports.jsx(s.code,{children:"ScenefileReader"})," with relevant information found in ",e.exports.jsx(s.code,{children:"src/parser/SceneData.h"}),". The important pieces are:"]}),`
205`,e.exports.jsxs(s.ol,{children:[`
206`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.code,{children:"SceneGlobalData"}),", which stores the global shading coefficients, essentially denoting how light interacts with the scene. You will learn more about these later in the course."]}),`
207`]}),`
208`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Extra: more info"}),e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line line-number",line:"37",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// Struct which contains the global color coefficients of a scene."}),`
209`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"38",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// These are multiplied with the object-specific materials in the lighting equation."}),`
210`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"39",children:[e.exports.jsx(s.span,{className:"pl-k",children:"struct"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"SceneGlobalData"}),`  {
211`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"40",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," ka; ",e.exports.jsx(s.span,{className:"pl-c",children:"// Ambient term"}),`
212`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"41",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," kd; ",e.exports.jsx(s.span,{className:"pl-c",children:"// Diffuse term"}),`
213`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"42",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," ks; ",e.exports.jsx(s.span,{className:"pl-c",children:"// Specular term"}),`
214`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"43",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," kt; ",e.exports.jsx(s.span,{className:"pl-c",children:"// Transparency; used for extra credit (refraction)"}),`
215`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"44",children:`};
216`})]})}),e.exports.jsxs(s.p,{children:[e.exports.jsx(s.code,{children:"SceneGlobalData"})," stores the global ambient, diffuse, and specular coefficients, as well as the transparency index of refraction. These are used to calculate how light interacts with the scene."]})]}),`
217`,e.exports.jsxs(s.ol,{start:"2",children:[`
218`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.code,{children:"SceneCameraData"}),", which stores the camera position, look, up, and field of view."]}),`
219`]}),`
220`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Extra: more info"}),e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line line-number",line:"63",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// Struct which contains data for the camera of a scene"}),`
221`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"64",children:[e.exports.jsx(s.span,{className:"pl-k",children:"struct"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"SceneCameraData"}),` {
222`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"65",children:`    glm::vec4 pos;
223`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"66",children:`    glm::vec4 look;
224`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"67",children:`    glm::vec4 up;
225`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"68",children:`
226`}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"69",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," heightAngle;   ",e.exports.jsx(s.span,{className:"pl-c",children:"// The height angle of the camera in RADIANS"}),`
227`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"70",children:`
228`}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"71",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," aperture;      ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable for depth of field"}),`
229`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"72",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," focalLength;   ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable for depth of field"}),`
230`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"73",children:`};
231`})]})}

231),e.exports.jsxs(s.p,{children:[e.exports.jsx(s.code,{children:"SceneCameraData"})," stores ",e.exports.jsx(s.code,{children:"pos"}),", ",e.exports.jsx(s.code,{children:"look"}),", and ",e.exports.jsx(s.code,{children:"up"})," in world space, so the view matrix can be built directly from those values. One important thing to note is that ",e.exports.jsx(s.code,{children:"pos"}),", ",e.exports.jsx(s.code,{children:"look"}),", and ",e.exports.jsx(s.code,{children:"up"})," are all defined in world space. They'd be pretty useless if they were defined in camera space."]})]}),`
232`,e.exports.jsxs(s.ol,{start:"3",children:[`
233`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.code,{children:"SceneLightData"}),", which stores the scene lights."]}),`
234`]}),`
235`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Extra: more info"}),e.exports.jsxs(s.p,{children:[e.exports.jsx(s.code,{children:"SceneLightData"})," supports point, directional, and spot lights. A point light has a position. A directional light has a direction. A spot light has both, plus cone parameters."]}),e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line line-number",line:"46",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// Struct which contains data for a single light"}),`
236`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"47",children:[e.exports.jsx(s.span,{className:"pl-k",children:"struct"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"SceneLightData"}),` {
237`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"48",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"int"}),` id;
238`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"49",children:`    LightType type;
239`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"50",children:`
240`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"51",children:`    SceneColor color;
241`}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"52",children:["    glm::vec3 function;  ",e.exports.jsx(s.span,{className:"pl-c",children:"// Attenuation function"}),`
242`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"53",children:`
243`}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"54",children:["    glm::vec4 pos;       ",e.exports.jsx(s.span,{className:"pl-c",children:"// Not applicable to directional lights"}),`
244`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"55",children:["    glm::vec4 dir;       ",e.exports.jsx(s.span,{className:"pl-c",children:"// Not applicable to point lights"}),`
245`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"56",children:`
246`}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"57",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," penumbra;      ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable to spot lights, in RADIANS"}),`
247`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"58",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," angle;         ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable to spot lights, in RADIANS"}),`
248`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"59",children:`};
249`})]})}),e.exports.jsxs(s.p,{children:["Each light in our scene is represented with a struct that includes its ",e.exports.jsx(s.code,{children:"LightType"}),", its color, and other relevant information depending on the ",e.exports.jsx(s.code,{children:"LightType"}),"."]}),e.exports.jsxs(s.ol,{children:[`
250`,e.exports.jsxs(s.li,{children:["A ",e.exports.jsx(s.strong,{children:"point light"})," is a single point in space that emits light equally in all directions (e.g. an infinitesimally small lightbulb). It is defined by its color and position."]}),`
251`,e.exports.jsxs(s.li,{children:["A ",e.exports.jsx(s.strong,{children:"directional light"})," is a global light which simulates light from a source that is infinitely far away (e.g. the sun, as we experience it on earth). It is defined by its color and direction."]}),`
252`,e.exports.jsxs(s.li,{children:["A ",e.exports.jsx(s.strong,{children:"spot light"})," is much more interesting\u2014it is effectively a point light, but it emits light only in a cone shape (e.g. a flashlight). It is defined by its color, position, and direction, as well as a penumbra and angle, which describe its cone.",`
253`,`
254`]}),`
255`]}),e.exports.jsxs(s.p,{children:["Documentation about virtual lights commonly used in 3D scenes can be readily found online, such as in the ",e.exports.jsx(s.a,{href:"https://docs.unity3d.com/Manual/Lighting.html",target:"_blank",rel:"noopener noreferrer",children:"Unity3D manual"}),"."]})]}),`
256`,e.exports.jsxs(s.ol,{start:"4",children:[`

257`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.code,{children:"ScenePrimitive"}),", which stores the primitive type, material, and optional mesh file."]}),`
258`]}),`
259`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Extra: more info"}),e.exports.jsxs(s.p,{children:[e.exports.jsx(s.code,{children:"ScenePrimitive"})," stores the primitive type and material. Mesh files are only needed for triangle meshes."]}),e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line line-number",line:"16",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// Enum of the types of primitives that might be in the scene"}),`
260`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"17",children:[e.exports.jsx(s.span,{className:"pl-k",children:"enum"})," ",e.exports.jsx(s.span,{className:"pl-k",children:"class"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"PrimitiveType"}),` {
261`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"18",children:`    PRIMITIVE_CUBE,
262`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"19",children:`    PRIMITIVE_CONE,
263`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"20",children:`    PRIMITIVE_CYLINDER,
264`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"21",children:`    PRIMITIVE_TORUS,
265`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"22",children:`    PRIMITIVE_SPHERE,
266`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"23",children:`    PRIMITIVE_MESH
267`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"24",children:`};
268`})]})}),e.exports.jsxs(s.p,{children:["Much like with ",e.exports.jsx(s.code,{children:"LightType"}),", we use ",e.exports.jsx(s.code,{children:"PrimitiveType"})," to identify different types of primitives. This is used in a struct, ",e.exports.jsx(s.code,{children:"ScenePrimitive"}),", to describe a specific primitive in the scene:"]}),e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line line-number",line:"130",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// Struct which contains data for a single primitive in a scene"}),`
269`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"131",children:[e.exports.jsx(s.span,{className:"pl-k",children:"struct"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"ScenePrimitive"}),` {
270`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"132",children:`   PrimitiveType type;
271`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"133",children:`   SceneMaterial material;
272`}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"134",children:["   std::string   meshfile; ",e.exports.jsx(s.span,{className:"pl-c",children:"// Used for triangle meshes"}),`
273`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"135",children:`};
274`})]})}),e.exports.jsxs(s.p,{children:["Every primitive has both a ",e.exports.jsx(s.code,{children:"type"})," and ",e.exports.jsx(s.code,{children:"material"}),". The ",e.exports.jsx(s.code,{children:"meshfile"})," field will only be relevant if you'd like to implement triangle mesh rendering, an extra credit option for our ",e.exports.jsx(s.strong,{children:"Ray"})," and ",e.exports.jsx(s.strong,{children:"Realtime"})," projects."]}),e.exports.jsxs(s.p,{children:[e.exports.jsx(s.code,{children:"material"})," contains important information about what the primitive looks like (e.g. its color, how shiny it is, any textures, etc.). You can look at the definition of ",e.exports.jsx(s.code,{children:"SceneMaterial"})," for details, but it's fine not to understand any of the terms which haven't yet been covered in lecture."]}),e.exports.jsxs(s.p,{children:["Observe that, unlike the light or camera structs, there aren't any fields in ",e.exports.jsx(s.code,{children:"ScenePrimitive"})," that describe its transformation. This is because it's more practical to use ",e.exports.jsx(s.strong,{children:"scene graphs"})," to manage this, especially when we have a lot of primitives!"]})]}),`
275`,e.exports.jsxs(s.ol,{start:"5",children:[`

276`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.code,{children:"SceneTransformation"}),", which stores translate, scale, rotate, or matrix transforms."]}),`
277`]}),`
278`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Extra: more info"}),e.exports.jsx(s.p,{children:"The parser uses four types of transformations:"}),e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line line-number",line:"26",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// Enum of the types of transformations that can be applied"}),`
279`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"27",children:[e.exports.jsx(s.span,{className:"pl-k",children:"enum"})," ",e.exports.jsx(s.span,{className:"pl-k",children:"class"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"TransformationType"}),` {
280`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"28",children:`    TRANSFORMATION_TRANSLATE,
281`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"29",children:`    TRANSFORMATION_SCALE,
282`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"30",children:`    TRANSFORMATION_ROTATE,
283`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"31",children:`    TRANSFORMATION_MATRIX
284`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"32",children:`};
285`})]})}),e.exports.jsxs(s.p,{children:[e.exports.jsx(s.code,{children:"SceneTransformation"})," stores the specific data for one transform:"]}),e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line line-number",line:"137",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// Struct which contains data for a transformation."}),`
286`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"138",children:[e.exports.jsx(s.span,{className:"pl-k",children:"struct"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"SceneTransformation"}),` {
287`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"139",children:`    TransformationType type;
288`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"140",children:`
289`}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"141",children:["    glm::vec3 translate; ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable when translating."}),`
290`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"142",children:["    glm::vec3 scale;     ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable when scaling."}),`
291`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"143",children:["    glm::vec3 rotate;    ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable when rotating."}),`
292`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"144",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"float"})," angle;         ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable when rotating."}),`
293`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"145",children:["    glm::mat4 matrix;    ",e.exports.jsx(s.span,{className:"pl-c",children:"// Only applicable when transforming by a custom matrix."}),`
294`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"146",children:`};
295`})]})})]}),`
296`,e.exports.jsxs(s.ol,{start:"6",children:[`
297`,e.exports.jsxs(s.li,{children:[e.exports.jsx(s.code,{children:"SceneNode"}),", which stores a list of transformations, primitives, and child nodes."]}),`
298`]}),`
299`,e.exports.jsxs("details",{children:[e.exports.jsx("summary",{children:"Extra: more info"}),e.exports.jsx(s.p,{children:"Our scene graph is composed of nodes, each of which describes zero or more of the following:"}),e.exports.jsxs(s.ol,{children:[`
300`,e.exports.jsx(s.li,{children:"a series of transformations,"}),`
301`,e.exports.jsx(s.li,{children:"a number of primitives, and"}),`
302`,e.exports.jsx(s.li,{children:"a number of child nodes."}),`
303`]}

303),e.exports.jsxs(s.p,{children:[e.exports.jsx(s.code,{children:"SceneNode"})," looks like this:"]}),e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line line-number",line:"148",children:[e.exports.jsx(s.span,{className:"pl-c",children:"// Struct which represents a node in the scene graph/tree, to be parsed by the student's `SceneParser`."}),`
304`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"149",children:[e.exports.jsx(s.span,{className:"pl-k",children:"struct"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"SceneNode"}),` {
305`]}),e.exports.jsxs(s.span,{className:"code-line line-number",line:"150",children:["   std::vector<SceneTransformation*> transformations; ",e.exports.jsx(s.span,{className:"pl-c",children:"// Note the order of transformations described in lab 4"}),`
306`]}),e.exports.jsx(s.span,{className:"code-line line-number",line:"151",children:`   std::vector<ScenePrimitive*>      primitives;
307`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"152",children:`   std::vector<SceneNode*>           children;
308`}),e.exports.jsx(s.span,{className:"code-line line-number",line:"153",children:`};
309`})]})}),e.exports.jsxs(s.p,{children:["If a ",e.exports.jsx(s.code,{children:"SceneNode"})," has transformations, those apply to both its primitives and children."]})]}),`
310`,e.exports.jsx(s.h3,{id:"scene-graphs",children:e.exports.jsx(s.a,{href:"#scene-graphs",children:"Scene Graphs"})}),`
311`,e.exports.jsx(s.p,{children:"Recall from earlier that the CTM (cumulative transformation matrix) of a primitive is the ordered product of all transformations from the root down to that primitive's node."}),`
312`,e.exports.jsxs(s.div,{className:"success-callout callout",children:[e.exports.jsx(s.p,{children:"Earlier, we chose TRS ordering when composing transformations. Here, the scene file has already fixed an order for each node."}),e.exports.jsx(s.p,{children:"Multiply transformations into the CTM in list order:"}),e.exports.jsx(s.pre,{className:"language-python",children:e.exports.jsxs(s.code,{className:"language-python code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line",children:["node.transformations ",e.exports.jsx(s.span,{className:"pl-k",children:"="}),` [t1, t2, t3]
313`]}),e.exports.jsxs(s.span,{className:"code-line",children:["ctm ",e.exports.jsx(s.span,{className:"pl-k",children:"="})," ctm ",e.exports.jsx(s.span,{className:"pl-k",children:"*"})," t1 ",e.exports.jsx(s.span,{className:"pl-k",children:"*"})," t2 ",e.exports.jsx(s.span,{className:"pl-k",children:"*"}),` t3
314`]})]})}),e.exports.jsxs(s.p,{children:["Because of how matrix-vector multiplication associates, this means the ",e.exports.jsx(s.em,{children:"last"})," transformation is actually applied to a point first, and the first one last."]})]}),`
315`,e.exports.jsx(s.h3,{id:"implementing-sceneparserparse",children:e.exports.jsxs(s.a,{href:"#implementing-sceneparserparse",children:["Implementing ",e.exports.jsx(s.code,{children:"SceneParser::parse()"})]})}),`
316`,e.exports.jsxs(s.p,{children:["Whenever we load a scene, we call ",e.exports.jsx(s.code,{children:"SceneParser::parse()"})," (located in ",e.exports.jsx(s.code,{children:"src/parsing/sceneparser.cpp"}),") to convert the scene data into render data."]}),`
317`,e.exports.jsx(s.pre,{className:"language-cpp",children:e.exports.jsxs(s.code,{className:"language-cpp code-highlight",children:[e.exports.jsxs(s.span,{className:"code-line",children:[e.exports.jsx(s.span,{className:"pl-k",children:"bool"})," ",e.exports.jsx(s.span,{className:"pl-en",children:"SceneParser::parse"}),`(std::string filepath, RenderData &renderData) {
318`]}),e.exports.jsxs(s.span,{className:"code-line",children:["    ScenefileReader fileReader = ",e.exports.jsx(s.span,{className:"pl-c1",children:"ScenefileReader"}),`(filepath);
319`]}),e.exports.jsxs(s.span,{className:"code-line",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"bool"})," success = fileReader.",e.exports.jsx(s.span,{className:"pl-c1",children:"readJSON"}),`();
320`]}),e.exports.jsxs(s.span,{className:"code-line",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"if"}),` (!success) {
321`]}),e.exports.jsxs(s.span,{className:"code-line",children:["        ",e.exports.jsx(s.span,{className:"pl-k",children:"return"})," ",e.exports.jsx(s.span,{className:"pl-c1",children:"false"}),`;
322`]}),e.exports.jsx(s.span,{className:"code-line",children:`    }
323`}),e.exports.jsx(s.span,{className:"code-line",children:`
324`}),e.exports.jsxs(s.span,{className:"code-line",children:["    ",e.exports.jsx(s.span,{className:"pl-c",children:"// Tasks"}),`
325`]}),e.exports.jsx(s.span,{className:"code-line",children:`
326`}),e.exports.jsxs(s.span,{className:"code-line",children:["    ",e.exports.jsx(s.span,{className:"pl-k",children:"return"})," ",e.exports.jsx(s.span,{className:"pl-c1",children:"true"}),`;
327`]}),e.exports.jsx(s.span,{className:"code-line",children:`}
328`})]})}),`
329`,e.exports.jsxs(s.p,{children:["The first step is to copy the global and camera data from ",e.exports.jsx(s.co

329de,{children:"fileReader"})," into ",e.exports.jsx(s.code,{children:"renderData"}),"."]}),`
330`,e.exports.jsx(s.div,{className:"task-callout callout",children:e.exports.jsxs(s.p,{children:["Use the ",e.exports.jsx(s.code,{children:"fileReader"})," methods to assign the scene's global data and camera data into ",e.exports.jsx(s.code,{children:"renderData"}),"."]})}),`
331`,e.exports.jsx(s.h3,{id:"traversing-the-scene-graph",children:e.exports.jsx(s.a,{href:"#traversing-the-scene-graph",children:"Traversing The Scene Graph"})}),`
332`,e.exports.jsxs(s.p,{children:["The next step is to traverse the scene graph, build cumulative transforms, and populate ",e.exports.jsx(s.code,{children:"renderData.shapes"})," and ",e.exports.jsx(s.code,{children:"renderData.lights"}),"."]}),`
333`,e.exports.jsx(s.div,{className:"success-callout callout",children:e.exports.jsx(s.p,{children:"Instead of walking back to the root every time we need a CTM, it is more efficient to build the cumulative transform as we descend the tree. That means passing the current transform down to each child and updating it as we go."})}),`
334`,e.exports.jsxs(s.div,{className:"task-callout callout",children:[e.exports.jsx(s.div,{className:"warning-callout callout",children:e.exports.jsx(s.p,{children:"This is a much bigger task than the others in this lab. If you get stuck, remember that you can collaborate with others in this course!"})}),e.exports.jsxs(s.p,{children:["Start by getting the root node from ",e.exports.jsx(s.code,{children:"fileReader"})," and clearing ",e.exports.jsx(s.code,{children:"renderData.shapes"}),"."]}),e.exports.jsxs(s.p,{children:["Then perform a depth-first traversal of the scene graph. As you traverse, keep a running cumulative transform. For each primitive you encounter, create a ",e.exports.jsx(s.code,{children:"RenderShapeData"})," with that primitive and its CTM, then append it to ",e.exports.jsx(s.code,{children:"renderData.shapes"}),"."]}),e.exports.jsxs(s.p,{children:["For each light you encounter, construct a ",e.exports.jsx(s.code,{children:"SceneLightData"})," and append it to ",e.exports.jsx(s.code,{children:"renderData.lights"}),". Light positions should be transformed as points, and directions should be transformed as vectors, both into world space."]}),e.exports.jsx(s.p,{children:"Use a recursive helper if that makes the traversal cleaner. Think carefully about which values should be passed by reference and which should be passed by value."}),e.exports.jsxs(s.blockquote,{children:[`
335`,e.exports.jsxs(s.p,{children:[e.exports.jsx(s.strong,{children:"Note:"})," Scene file rotations are specified as an arbitrary axis (",e.exports.jsx(s.code,{children:"glm::vec3"}),") and angle, not necessarily aligned to X, Y, or Z. Your earlier ",e.exports.jsx(s.code,{children:"getRotationMatrixX/Y/Z"})," functions will not work for this purpose. You are allowed and encouraged to use the built-in ",e.exports.jsx(s.code,{children:"glm"})," functions for building transformation matrices. You may find ",e.exports.jsx(s.code,{children:"glm::translate"}),", ",e.exports.jsx(s.code,{children:"glm::scale"}),", and ",e.exports.jsx(s.code,{children:"glm::rotate"})," useful for building the matrices for each transformation."]}),`
336`]})]}),`
337`,e.exports.jsx(s.h3,{id:"testing-scenes",children:e.exports.jsx(s.a,{href:"#testing-scenes",children:"Testing Scenes"})}),`
338`,e.exports.jsxs(s.p,{children:["Once your parser is wired up, you should be able to load scenefiles like ",e.exports.jsx(s.code,{children:"directional_light_1.json"}),", ",e.exports.jsx(s.code,{children:"ambient_total.json"}),", and ",e.exports.jsx(s.code,{children:"primitive_salad_1.json"})," (all located in ",e.exports.jsx(s.code,{children:"resources/scenefiles/"}),")."]}),`
339`,e.exports.jsx(t,{images:[{src:"/labs/lab3/direction-light-expected.png",alt:"TODO"},{src:"/labs/lab3/ambient-total-expected.png",alt:"TODO"},{src:"/labs/lab3/primitive-salad-expected.png",alt:"TODO"}],figNumber:19,figCaption:"What you should see if your parser can load the sample scenes correctly."}),`
340`,e.exports.jsx(s.p,{children:"Loading a scene helps verify that the camera, primitives, and transformations are correct. The lighting support code is intentionally basic, so this does not fully validate every light-related detail."}),`
341`,e.exports.jsx(s.h2,{id:"end",children:e.exports.jsx(s.a,{href:"#end",children:"End"})}),`
342`,e.exports.jsx(s.p,{children:"Congrats on finishing the transforms and parsing lab! By this point, you should be able to explain the transformation rules, the camera view matrix, and how a scene graph becomes render data."}),`
343`,e.exports.jsx(s.h2,{id:"submission",children:e.exports.jsx(s.a,{href:"#submission",children:"Submission"})}),`
344`,e.exports.jsx(s.p,{children:"Submit your GitHub link and commit ID to the combined lab assignment on Gradescope, then get checked off by a TA at hours."}),`
345`,e.exports.jsxs(s.p,{children:["Reference the GitHub + Gradescope Guide ",e.exports.jsx(s.a,{href:"/docs/github-gradescope-guide#handing-in-assignments",children:"here"}),"."]}),`
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