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
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
COMPUTER GRAPHICS
Mubbasir Kapadia
cs.rutgers.edu/~mubbasir/
Email: [email protected]
Office: CBIM 10
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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
Addi
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 value
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 sys