CS 354 Procedural Methods; April 3, 2012; University of Texas at Austin

1. CS 354
Procedural Methods
Mark Kilgard
University of Texas
April 3, 2012

2. CS 354 2
Today’s material
 In-class quiz
 On interaction lecture
 Lecture topic
 Project 2
 Procedural methods

3. CS 354 3
My Office Hours
 Tuesday, before class
 Painter (PAI) 5.35
 8:45 a.m. to 9:15
 Thursday, after class
 ACE 6.302
 11:00 a.m. to 12
 Randy’s office hours
 Monday & Wednesday
 11 a.m. to 12:00
 Painter (PAI) 5.33

4. CS 354 4
Last time, this time
 Last lecture, we discussed
 Project 2 on Programmable Shaders
 Interaction
 Event models
 Buffering frames
 This lecture
 Project 2 discussion
 Procedural methods for texturing and modeling
 Intermediate milestone for Project 2 due
 Had to first 2 shader tasks done
 Deadline was yesterday
 All shaders due Friday, April 6th

5. CS 354 5
On a sheet of paper
Daily Quiz • Write your EID, name, and date
• Write #1, #2, #3, #4 followed by its answer
 Multiple choice: Which one of  True or False: Tearing is a
these is not an interactive event display artifact that results
processing model? from unsynchronized buffer
swap or blit operations.
a) Batching
b) Polling
 Multiple choice: Triple
buffering can improve display
c) Event-driven update latency but suffers
from:
 True or False: GLUT a) Requiring additional buffer
programs receive events memory
through callback functions.
b) May render frames that
are never actually displayed
c) Both a) and b)
d) Neither a) nor b)

6. CS 354 6
Project 2
 Project is NOW available
 PDF + code to use
 Requirements
 Mostly writing GLSL shaders
 Small amount of C/C++ code
 Convert height map to normal map
 Implement NormalMap::computeNormal method
 Intermediate milestone
 Yesterday: Monday, April 2nd
 Submit snapshots and GLSL code for first two shaders
 Complete project
 Due Friday, April 6th
 All 10 shaders
 Embellish for additional credit

7. CS 354 7
Your Mission So Far
 You should now have these first two
shaders tasks implemented
Task 1: apply decal
Task 0: roll torus

8. CS 354 8
Procedurally Generating a
Torus from a 2D Grid
2D grid over (s,t)∈[0,1]
Tessellated torus

9. CS 354 9
GLSL Standard Library Routines
You’ll Need for Project 2
 texture2D—accesses a 2D texture through a sampler2D and a 2-component
texture coordinate set (s,t)
 textureCube—access a cube map with a samplerCube and a 3-component
texture coordinate set (s,t,r)
 normalize—normalizes a vector
 cross—computes a cross product of 2 vectors
 dot—computes a dot (inner) product of 2 vectors
 max—compute the maximum of two values
 reflect—compute a reflection vector given an incident vector and a normal
vector
 vec3—constructor for 3-component vector from scalars
 mat3—constructor for 3x3 matrix from column vectors
 *—matrix-by-vector or vector-by-matrix multiplication
 sin—sine trigonometric function
 cos—cosine trigonometric function
 pow—raise a number to a power, exponentiation (hint: specular)

10. CS 354 10
Coordinate Spaces for Project 2
 Parametric space
 2D space [0..1]x[0..1] for 2D patch
 Object space
 Transform the patch’s parametric space into a 3D space
containing a torus
 Has modeling transformation from object- to world-space
 World space
 Environment map is oriented in this space
 gluLookAt’s coordinates are in this space
 Surface space
 (0,0,1) is always surface normal direction
 Mapping from object space to surface space varies along torus
 Perturbed normal from normal map overrides (0,0,1) geometric
normal
 Eye space
 gluLookAt transforms world space to eye space

11. CS 354 11
Artist-driven
Content Generation
 Advantages
 Human artistic expression!
 Human-to-human user interface
 Polish
 Disadvantages
 Human-intensive
 Takes time to make lots of it
 Involved to change
 Data intensive

12. CS 354 12
Image-driven
Content Generation
 Advantages
 As easy as taking pictures
 Disadvantages
 Very data-intensive
 Calibrating cameras & correlating images
 Quite involved
image panorama
 Involved to edit

13. CS 354 13
Procedural
Texturing and Modeling
 Let programs generate content!
 Advantages
 Small programs → lots of content
 Compact storage requirements
 Easy to generate more content
 Disadvantages
 Hard to control exactly

14. CS 354 14
Iterated Functions
 Provides infinite detail
Example:
Fractal Mandelbrot set

15. CS 354 15
Generating Lots of Content
Procedurally

16. CS 354 16
L-Systems
 Developed by Aristid Lindenmayer
 Theoretical biologist
 Hence the L in L-System
 Concept
 Use a rewriting system to model growth and
morphology of biological organisms
 Components
 Axiom – initial state
 Generator – applied recursively
 Useful in non-biology contexts too
 Geology, man-made objects, etc.

17. CS 354 17
Sierpinski Gasket
Rule based:
Repeat n times. As n →∞
Area→0
Perimeter →∞
Not a normal geometric object

18. CS 354 18
Apply Sierpinski Gasket Rules
Recursively

19. CS 354 19
Snow Flake Curve

20. CS 354 20
Other Axioms & Generators

21. CS 354 21
Tree Generation
An axial tree Sample tree generated from
branching patterns

22. CS 354 22
Plant Generation Rules

23. CS 354 23
Stochastic L-systems
 Probabilistic
Stochastic L-systems can
generate natural variations

24. CS 354 24
More Plant Generation Rules

25. CS 354 25
Fractal Mountains
[Przemyslaw Prusinkiewicz & Mark Hammel, 1993]

26. CS 354 26
Different Fractal Mountains

27. CS 354 27
Domain-specific Procedural
Artistry Tools

28. CS 354 28
Trees Really Matter
 Commercial product SpeedTree specializes at
drawing realistic trees fast

29. CS 354 29
Biological Inspiration
 Pseudo-Darwinian animation evolution

30. CS 354 30
Procedural Generation of
Buildings
 Buildings have rules too
 Doors, windows, facades
 Consistency of style
 Instant Architecture
façade derivation…

31. CS 354 31
Procedural Generation of Cities!
 Cities are very detailed and complex
 CityGen
 But follow regular rules – roads, blocks, respecting
topography, etc.

32. CS 354 32
Particle Systems

33. CS 354 33
Particle Systems and
Their Equations
pi = (xi, yi zi)
vi = dpi /dt = pi‘ = (dxi /dt, dyi /dt , zi /dt)
m vi‘= fi
Hard part is defining force vector
33

34. CS 354 34
Force Vector
 Independent Particles
 Gravity
 Wind forces
 O(n) calulation
 Coupled Particles O(n)
 Meshes
 Spring-Mass Systems
 Coupled Particles O(n2)
 Attractive and repulsive forces
34

35. CS 354 35
Solution of Particle Systems
float time, delta state[6n], force[3n];
state = initial_state();
for(time = t0; time<final_time, time+=delta) {
force = force_function(state, time);
state = ode(force, state, time, delta);
render(state, time)
}
35

36. CS 354 36
Simple Forces
 Consider force on particle i
fi = fi(pi, vi)
 Gravity fi = g
gi = (0, -g, 0)
 Wind forces
 Drag
pi(t0), vi(t0)
36

37. CS 354 37
Attraction and Repulsion
 Inverse square law
f = -krd/|d|3
 General case requires O(n2) calculation
 In most problems, the drop off is such that
not many particles contribute to the forces
on any given particle
 Sorting problem: is it O(n log n)?
E. Angel and D. Shreiner: Interactive Computer Graphics 6E © Addison-Wesley 2012 37

38. CS 354 38
Noise Textures
 Invented by Ken Perlin
 Academy Award winning idea
 A texturing primitive
 Basis for “natural” looking textures and
phenomenon
 No memory/bandwidth requirements
 Computed on the fly; no “source image”
 No mapping problem
 Naturally 3D so not prone to “gift wrapping” issues
 Useful for range of applications and
effects

39. CS 354 39
What is Noise?
 Band-limited repeatable
pseudo-random function
 Domain: Rn
 Approximate to Gaussian filtered
random noise
 Implemented as a pseudo-
random spline
 On regular grid
Marble vase
generated with
Perlin noise

40. CS 354 40
Variations on Noise
 Use noise within other functions
turbulence

41. CS 354 41
Combining Noise Patterns
 Sum noise patterns
 As frequency doubles, amplitude halves

42. CS 354 42
Turbulence
 Simulate turbulence by generating noise at
different octaves (scales)
 Average those octaves:

43. CS 354 43
Generating Marble Pattern
 Start with sine pattern in solid texture
 Then add turbulence
 Looks like veins in marble

44. CS 354 44
Variations on Marble
 Scale the magnitude of the turbulence
displacing the sine pattern

45. CS 354 45
Wood Pattern
 Start with cylindrical pattern
 Compute sine of distance from center of cylinder
 Interpolate between dark and light brown color

46. CS 354 46
Irregular Wood Rings
 Now use small amount of turbulence to displace
the tree rings in the wood
 Much less turbulence than marble case
 To preserve the rings

47. CS 354 47
Irregular Wood Grain
 Also want turbulence in Z direction but scale it
back to preserve the grain
less turbulence in z

48. CS 354 48
Shading with
Marble and Wood

49. CS 354 49
Other Procedurally Modeled
Phenomenon
 Smoke
 Difficult for an artist to model
 Needs to billow and flow around objects

50. CS 354 50
Entire Book on
Procedural Techniques
David Ebert,
Ken Musgrave,
Darwyn Peachey,
Ken Perlin,
Steve Worley

51. CS 354 51
Next Class
 Next lecture
 Bezier curves
 How do we move smoothly and simply with control?
 Project 2
 Shading and lighting with GLSL
 Due Friday, April 6th