Linear Harmonic Oscillator
It appears in many places in graphics
Spring-mass systems
Muscle (motor) modeling
Mocap tracking
PD control
Quiz: What is the difference between these springs ?
General Form
Example of a physical equivalent
1D Particle with
Summary
General form of the splines we have seen
Often f is a translated version of a single function
Note: P can be any dimension, typically 1,2, or 3
KEEP IN MIND!
To simplify the math the formulas assume
L+1 control points.
B-Splines
Well drop the inte
COMPUTER GRAPHICS
Mubbasir Kapadia
cs.rutgers.edu/~mubbasir/
Email: [email protected]
Office: CBIM 10
STAR: State of the Art Report
- Topic Preferences
- Pick your topic today!
- Due Tue 5 pm.
- LATEX
- LATEX template will be provided
- Large
Vectors
N-tuple:
Vectors
N-tuple:
Magnitude:
Unit vectors
Normalizing a vector
Operations with vectors
Addition
Multiplication with scalar (scaling)
Properties
Visualization for 2D and 3D vectors
Addition
Scaling
Subtraction
Adding the negatively scaled v
Splines and Motion Curves
Many kinds of curves
Sinusoidal
Exponential
Complex
Fractals
Polynomials
Combinations
Different forms of curve
functions
Explicit: y = f(x), z=g(x)
Cannot get multiple values for single x, infinite slopes
Implicit: f(x,y,z) = 0
Collisions
Reference: http:/www.toptal.com/game/video-game-physics-part-ii-collision-detection-for-solidobjects
Linear Algebra Primer: http:/www.toptal.com/game/video-game-physics-part-i-an-introductionto-rigid-body-dynamics#appendix
Collisions in Video G
Particle systems
From Feldman, B. E., O'Brien, J. F., Arikan, O., "Animating Suspended Particle
Explosions." The Proceedings of ACM SIGGRAPH 2003, San Diego, California,
July, pp. 708-715
Particle systems
Used to model particle-like stuff
Dust, sparks, f