lecture 1: course intro -...
TRANSCRIPT
![Page 1: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/1.jpg)
Computer Graphics CMU 15-462/662, Spring 2019
Lecture 1:
Course Intro: Welcome to Computer Graphics!
![Page 2: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/2.jpg)
CMU 15-462/662, Spring 2019
Hi!Adrian Biagioli
Connor Lin
Nancy Pollard
Yuqiao Zeng
![Page 3: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/3.jpg)
CMU 15-462/662, Spring 2019
What is computer graphics?
com•put•er graph•ics /kəmˈpyoodər ˈɡrafiks/ n. The use of computers to synthesize and manipulate visual information.
![Page 4: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/4.jpg)
CMU 15-462/662, Spring 2019
Why visual information?
(Allan Ajifo)(Petar Milošević)
About 30% of brain dedicated to visual processing...
...eyes are highest-bandwidth port into the head!
![Page 5: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/5.jpg)
CMU 15-462/662, Spring 2019
Humans are visual creatures!
![Page 6: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/6.jpg)
CMU 15-462/662, Spring 2019
History of visual depictionHumans have always been visual creatures!
Indonesian cave painting (~38,000 BCE)
![Page 7: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/7.jpg)
CMU 15-462/662, Spring 2019
Visual technology: painting / illustrationNot purely representational: ideas, feelings, data, ...
![Page 8: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/8.jpg)
CMU 15-462/662, Spring 2019
Visual technology: carving / sculpture
![Page 9: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/9.jpg)
CMU 15-462/662, Spring 2019
Visual technology: photography / imagingProcessing of visual data no longer happening in the head!
Joseph Niépce, “View from the Window at Le Gras” (1826)
![Page 10: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/10.jpg)
CMU 15-462/662, Spring 2019
Visual technology: photography / imaging
![Page 11: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/11.jpg)
CMU 15-462/662, Spring 2019
Visual technology: digital imageryIntersection of visual depiction & computation
Ivan Sutherland, “Sketchpad” (1963)
![Page 12: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/12.jpg)
CMU 15-462/662, Spring 2019
Visual technology: digital imagery
![Page 13: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/13.jpg)
CMU 15-462/662, Spring 2019
Visual technology: 3D fabricationCreate physical realization of digital shape
A.J. Herbert / 3M (1979)
![Page 14: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/14.jpg)
CMU 15-462/662, Spring 2019
Visual technology: 3D fabrication
![Page 15: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/15.jpg)
CMU 15-462/662, Spring 2019
Technologies for visual depictionDrawing/painting/illustration (~40,000 BCE) Sculpture (~40,000 BCE) Photography (~1826) Digital Imagery (~1963) 3D Fabrication (~1979)
![Page 16: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/16.jpg)
CMU 15-462/662, Spring 2019
Definition of Graphics, Revisited
com•put•er graph•ics /kəmˈpyoodər ˈɡrafiks/ n. The use of computers to synthesize and manipulate visual information.
Why only visual?
![Page 17: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/17.jpg)
CMU 15-462/662, Spring 2019
Graphics as Synthesis of Sensory Stimuli
com•put•er graph•ics /kəmˈpyoodər ˈɡrafiks/ n. The use of computers to synthesize and manipulate sensory information.
(sound) (touch)
(…What about taste? Smell?!)
![Page 18: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/18.jpg)
CMU 15-462/662, Spring 2019
Computer graphics is everywhere!
![Page 19: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/19.jpg)
CMU 15-462/662, Spring 2019
Entertainment (movies, games)
![Page 20: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/20.jpg)
CMU 15-462/662, Spring 2019
EntertainmentNot just cartoons!
![Page 21: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/21.jpg)
CMU 15-462/662, Spring 2019
Art and design
![Page 22: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/22.jpg)
CMU 15-462/662, Spring 2019
Industrial design
![Page 23: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/23.jpg)
CMU 15-462/662, Spring 2019
Computer aided engineering (CAE)
![Page 24: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/24.jpg)
CMU 15-462/662, Spring 2019
Architecture
![Page 25: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/25.jpg)
CMU 15-462/662, Spring 2019
Scientific/mathematical visualization
![Page 26: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/26.jpg)
CMU 15-462/662, Spring 2019
Medical/anatomical visualization
![Page 27: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/27.jpg)
CMU 15-462/662, Spring 2019
Navigation
![Page 28: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/28.jpg)
CMU 15-462/662, Spring 2019
Communication
![Page 29: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/29.jpg)
CMU 15-462/662, Spring 2019
Foundations of computer graphicsAll these applications demand sophisticated theory & systems Theory - geometric representations - sampling theory - integration and optimization - radiometry - perception and color Systems - parallel, heterogeneous processing - graphics-specific programming languages
![Page 30: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/30.jpg)
CMU 15-462/662, Spring 2019
ACTIVITY: modeling and drawing a cubeGoal: generate a realistic drawing of a cube Key questions: - Modeling: how do we describe the cube? - Rendering: how do we then visualize this model?
![Page 31: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/31.jpg)
CMU 15-462/662, Spring 2019
ACTIVITY: modeling the cubeSuppose our cube is... - centered at the origin (0,0,0) - has dimensions 2x2x2 - edges are aligned with x/y/z axes QUESTION: What are the coordinates of the cube vertices?
A: ( 1, 1, 1 ) E: ( 1, 1,-1 )B: (-1, 1, 1 ) F: (-1, 1,-1 )C: ( 1,-1, 1 ) G: ( 1,-1,-1 )D: (-1,-1, 1 ) H: (-1,-1,-1 )
QUESTION: What about the edges?AB, CD, EF, GH,AC, BD, EG, FH,AE, CG, BF, DH
![Page 32: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/32.jpg)
CMU 15-462/662, Spring 2019
ACTIVITY: drawing the cubeNow have a digital description of the cube:VERTICESA: ( 1, 1, 1 ) E: ( 1, 1,-1 )B: (-1, 1, 1 ) F: (-1, 1,-1 )C: ( 1,-1, 1 ) G: ( 1,-1,-1 )D: (-1,-1, 1 ) H: (-1,-1,-1 )
How do we draw this 3D cube as a 2D (flat) image? Basic strategy: 1. map 3D vertices to 2D points in the image 2. connect 2D points with straight lines ...Ok, but how?
EDGES
AB, CD, EF, GH,AC, BD, EG, FH,AE, CG, BF, DH
![Page 33: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/33.jpg)
CMU 15-462/662, Spring 2019
Perspective projectionObjects look smaller as they get further away (“perspective”) Why does this happen? Consider simple (“pinhole”) model of a camera:
2D image
3D object
camera
![Page 34: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/34.jpg)
CMU 15-462/662, Spring 2019
Perspective projection: side viewWhere exactly does a point p = (x,y,z) end up on the image? Let’s call the image point q=(u,v)
p=(x,y,z)
q=(u,v) 3D object
imag
e
![Page 35: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/35.jpg)
CMU 15-462/662, Spring 2019
Perspective projection: side viewWhere exactly does a point p = (x,y,z) end up on the image? Let’s call the image point q=(u,v) Notice two similar triangles: p=(x,y,z)
q=(u,v)
1z
y
v 3D object
imag
e
Assume camera has unit size, origin is at pinhole c Then v/1 = y/z, i.e., vertical coordinate is just the slope y/z Likewise, horizontal coordinate is u=x/z
c
![Page 36: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/36.jpg)
CMU 15-462/662, Spring 2019
ACTIVITY: now draw it!Need 12 volunteers - each person will draw one cube edge - assume camera is at c=(2,3,5) - convert (X,Y,Z) of both endpoints to (u,v):
1. subtract camera c from vertex (X,Y,Z) to get (x,y,z) 2. divide (x,y) by z to get (u,v)—write as a fraction
- draw line between (u1,v1) and (u2,v2)
VERTICESA: ( 1, 1, 1 ) E: ( 1, 1,-1 )B: (-1, 1, 1 ) F: (-1, 1,-1 )C: ( 1,-1, 1 ) G: ( 1,-1,-1 )D: (-1,-1, 1 ) H: (-1,-1,-1 )
EDGES
AB, CD, EF, GH,AC, BD, EG, FH,AE, CG, BF, DH
![Page 37: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/37.jpg)
CMU 15-462/662, Spring 2019
ACTIVITY: output on graph paper
0 112
16
14
13
512
12
712
23
34
56
1112
10
112
16
14
13
512
12
712
23
34
56
1112
1
![Page 38: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/38.jpg)
CMU 15-462/662, Spring 2019
ACTIVITY: How did we do?
0 112
16
14
13
512
12
712
23
34
56
1112
10
112
16
14
13
512
12
712
23
34
56
1112
1
A: 1/4, 1/2B: 3/4, 1/2C: 1/4, 1D: 3/4, 1E: 1/6, 1/3F: 1/2, 1/3G: 1/6, 2/3H: 1/2, 2/3
2D coordinates:
![Page 39: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/39.jpg)
CMU 15-462/662, Spring 2019
ACTIVITY: Previous year’s result
![Page 40: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/40.jpg)
CMU 15-462/662, Spring 2019
But wait… How do we draw lines on a computer?
![Page 41: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/41.jpg)
CMU 15-462/662, Spring 2019
Close up photo of pixels on a modern display
![Page 42: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/42.jpg)
CMU 15-462/662, Spring 2019
Output for a raster displayCommon abstraction of a raster display: - Image represented as a 2D grid of “pixels” (picture elements) ** - Each pixel can can take on a unique color value
** We will strongly challenge this notion of a pixel “as a little square” soon enough. But let’s go with it for now. ;-)
![Page 43: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/43.jpg)
CMU 15-462/662, Spring 2019
What pixels should we color in to depict a line?“Rasterization”: process of converting a continuous object to a discrete representation on a raster grid (pixel grid)
![Page 44: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/44.jpg)
CMU 15-462/662, Spring 2019
What pixels should we color in to depict a line?
Light up all pixels intersected by the line?
![Page 45: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/45.jpg)
CMU 15-462/662, Spring 2019
What pixels should we color in to depict a line?Diamond rule (used by modern GPUs):
light up pixel if line passes through associated diamond
![Page 46: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/46.jpg)
CMU 15-462/662, Spring 2019
What pixels should we color in to depict a line?Is there a right answer?
(consider a drawing a “line” with thickness)
![Page 47: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/47.jpg)
CMU 15-462/662, Spring 2019
How do we find the pixels satisfying a chosen rasterization rule?
Could check every single pixel in the image to see if it meets the condition...
- O(n2) pixels in image vs. at most O(n) “lit up” pixels
- must be able to do better! (e.g., work proportional to number of pixels in the drawing of the line)
![Page 48: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/48.jpg)
CMU 15-462/662, Spring 2019
Incremental line rasterizationLet’s say a line is represented with integer endpoints: (u1,v1), (u2,v2) Slope of line: s = (v2-v1) / (u2-u1) Consider a very easy special case: - u1 < u2, v1 < v2 (line points toward upper-right) - 0 < s < 1 (more change in x than y)
v = v1;for( u=u1; u<=u2; u++ ){ v += s; draw( u, round(v) )}
Common optimization: rewrite algorithm to use only integer arithmetic (Bresenham algorithm)
u1 u2
v1
v2
Assume integer coordinates are at pixel centers
(u1,v1)
(u2,v2)
![Page 49: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/49.jpg)
CMU 15-462/662, Spring 2019
Our line drawing!
0 112
16
14
13
512
12
712
23
34
56
1112
10
112
16
14
13
512
12
712
23
34
56
1112
1
A: 1/4, 1/2B: 3/4, 1/2C: 1/4, 1D: 3/4, 1E: 1/6, 1/3F: 1/2, 1/3G: 1/6, 2/3H: 1/2, 2/3
2D coordinates:
![Page 50: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/50.jpg)
CMU 15-462/662, Spring 2019
We just rendered a simple line drawing of a cube.
But to render more realistic pictures (or animations) we need a much richer model
of the world.
surfaces motion
materials lights
cameras
![Page 51: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/51.jpg)
CMU 15-462/662, Spring 2019
2D shapes
patches may overlap a color sample so depth samples from differ-ent patches always compare with the latter patch in render order“winning”.
Prior to rendering any set of patches, a depth clear to zero is neces-sary to reset the depth buffer. This could be done with a “cover” op-eration that simply zeros the depth buffer (without modifying otherbuffers) or with a scissored depth buffer clear.
Once the render order issues are resolved, color shading is a matterof bicubic interpolation [Sun et al. 2007] in the TES.
This is a lot of complexity to match the PDF specification’s patchrendering order. Certainly if the hardware’s tessellation generatorsimply guaranteed an order consistent with the PDF specification,even at the cost of some less optimal hardware efficiency, renderingPDF gradient meshes would be much more straightforward.
Another option is detecting via CPU preprocessing of the patchmesh whether or not actual mesh overlaps are present [Randria-narivony and Brunnett 2004]. When not present, gradient meshrendering could be much more straightforward and efficient. Inpractice, we know overlaps are rare in real gradient mesh content.
Coarse Level-of-detail Control Graphics hardware tessellationhas a limited maximum level-of-detail for tessellation. When thelevel-of-detail is clamped to a hardware limit for tessellation, tes-sellation artifacts may arise. We monitor the relative size of tes-sellated patches such that their maximum level-of-detail does notgrossly exceed the scale of two or three pixels in window space.If this happens, patches need to be subdivided manually to ensurethe patch mesh avoids objectionable tessellation artifacts. Care isnecessary to maintain a water-tight subdivided patch mesh. This isdone by ensuring exactly matching level-of-detail computations onmutual edges of adjacent patches.
8 Comparing GPU versus CPU Rendering
Our contributions for GPU-acceleration are best understood in con-trast with Illustrator’s pre-existing CPU rendering approach. Allbut a cursory description of Illustrator’s CPU rendering approach isbeyond the scope of this paper. Illustrator’s CPU rendering closelyfollows the PDF standard [Adobe Systems 2008]. AGM’s CPUrenderer relies on a robust, expertly-tuned, but reasonably conven-tional active edge list algorithm [Foley et al. 1990] for rasterizingarbitrary paths including Bezier segments [Turner 2007]. Table 1lists the differences between the CPU and GPU approaches in orga-nizing the framebuffer storage for rendering. Table 2 lists the waysrendering is different between the CPU and GPU approaches.
9 Performance
We benchmarked our GPU-accelerated rendering mode againstAGM’s CPU-based renderer on six Illustrator documents picturedin Figure 10. We selected these scenes for their availability, artisticcontent, and complexity. Table 3 quantitatively summarizes eachscene’s complexity. We consider these scenes representative of thekind of complex artwork we wish to encourage by making its au-thoring more interactive.
9.1 Benchmarking RGB Artwork
Table 4 presents our benchmarking results for RGB color modelrendering. Our benchmarking method executes a script that zoomsand pans over the content to mimic the kind of fast view changes an
(a) WF BambooScene.ai
(b) archerfish.ai (c) Blue Mirror.ai
(d) whale2.ai
(e) Tropical Reef.ai
(f) bigBlend2.ai
Figure 10: Challenging Illustrator artwork for benchmarking.
146:10 • V. Batra et al.
ACM Transactions on Graphics, Vol. 34, No. 4, Article 146, Publication Date: August 2015
[Source: Batra 2017]
![Page 52: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/52.jpg)
CMU 15-462/662, Spring 2019
(Stanislav Orekhov)
Complex 3D surfaces
[Kaldor 2008]
![Page 53: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/53.jpg)
CMU 15-462/662, Spring 2019
Modeling material properties
[Jakob 2014]
[Wann Jensen 2001]
[Zhao 2013]
![Page 54: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/54.jpg)
CMU 15-462/662, Spring 2019
Realistic lighting environments Up, (Pixar 2009)
![Page 55: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/55.jpg)
CMU 15-462/662, Spring 2019
Realistic lighting environments Toy Story 3 (Pixar 2010)
![Page 56: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/56.jpg)
CMU 15-462/662, Spring 2019
Realistic lighting environments Big Hero 6 (Disney 2014)
![Page 57: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/57.jpg)
CMU 15-462/662, Spring 2019
This image is rendered in real-time on a modern GPU
Unreal Engine Kite Demo (Epic Games 2015)
![Page 58: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/58.jpg)
CMU 15-462/662, Spring 2019
[Mirror’s Edge 2008]
So is this.
![Page 59: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/59.jpg)
CMU 15-462/662, Spring 2019
Animation: modeling motion
https://www.youtube.com/watch?v=6G3O60o5U7w
Luxo Jr. (Pixar 1986)
![Page 60: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/60.jpg)
CMU 15-462/662, Spring 2019
Physically-based simulation of motion
https://www.youtube.com/watch?v=tT81VPk_ukU [James 2004]
![Page 61: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/61.jpg)
CMU 15-462/662, Spring 2019
Course Logistics
![Page 62: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/62.jpg)
CMU 15-462/662, Spring 2019
About this courseA broad overview of major topics and techniques in computer graphics: geometry, rendering, animation, imaging
Outline: - Focus on fundamental data structures and algorithms that
are reused across all areas of graphics - Assignments on:
- Rasterization - Geometric Modeling - Photorealistic Rendering - Animation
- In-class midterm/final
![Page 63: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/63.jpg)
CMU 15-462/662, Spring 2019
Assignment 0: Math (P)Review
![Page 64: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/64.jpg)
CMU 15-462/662, Spring 2019
Assignment 1: Rasterization
![Page 65: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/65.jpg)
CMU 15-462/662, Spring 2019
Assignment 2: Geometric Modeling
![Page 66: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/66.jpg)
CMU 15-462/662, Spring 2019
Assignment 3: Photorealistic Rendering
![Page 67: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/67.jpg)
CMU 15-462/662, Spring 2019
Assignment 4: Animation
(cribbed from Alec Jacobson)
![Page 68: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/68.jpg)
CMU 15-462/662, Spring 2019
Midterm / Final
Both cover cumulative material seen so far In-class, proctored exam Can bring one sticky note (both sides) w/ any information on it
![Page 69: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/69.jpg)
CMU 15-462/662, Spring 2019
Getting started
Create an account on the course web site: http://15462.courses.cs.cmu.edu/spring2019/home
Sign up for the course on Piazza https://piazza.com/class/jqv79wkbxqz743
There is no textbook for this course, but see the course website for references (there are some excellent graphics textbooks, some completely online!)
![Page 70: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/70.jpg)
CMU 15-462/662, Spring 2019
Assignments / Grading(10%) Warm-up Math (P)Review - Written exercises on basic linear algebra and vector calc. (individually)
(60%) Four programming assignments - Four programming assignments - Each worth 15% of overall course grade
(25%) Midterm / final - Both cover cumulative material seen so far
(5%) Class participation - In-class/website comments, other contributions to class
![Page 71: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/71.jpg)
CMU 15-462/662, Spring 2019
Late hand-in policy
Programming assignments - Five late day points for the semester - First three programming assignments only - No more late points? 10% penalty per day - No assignments will be accepted more than 3 days past the deadline
![Page 72: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/72.jpg)
CMU 15-462/662, Spring 2019
Cheating Policy
Let’s keep it simple: if you are caught cheating, you will get a zero for the entire course (not just the assignment).
![Page 73: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/73.jpg)
CMU 15-462/662, Spring 2019
The course web siteWe have no textbook for this class —the lecture slides and instructor/TA/student discussions on the web are the primary course reference
Slide comments and discussion
“Add private note” button: You can add notes to yourself about this slide here.
![Page 74: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/74.jpg)
CMU 15-462/662, Spring 2019
Our philosophy
We want a very active class: come to class, participate in the class, contribute to the web site
Challenging assignments (with tons of “going further” opportunities: see what you can do!)
Challenging exams (see what you can do!)
Very reasonable grading (at least the instructors think so)
![Page 75: Lecture 1: Course Intro - 15462.courses.cs.cmu.edu15462.courses.cs.cmu.edu/spring2019content/lectures/01_intro/01_intro... · CMU 15-462/662, Spring 2019 2D shapes patches may overlap](https://reader033.vdocuments.mx/reader033/viewer/2022050718/5e16f8bd7a020821b76a4327/html5/thumbnails/75.jpg)
CMU 15-462/662, Spring 2019
Next time, we’ll do a math review & preview - Linear algebra, vector calculus - Help make the rest of the course easier!
See you next time!