GLboids: Devlog 1

Arrian Chi
Jan 18, 2024 1 min read

Interpolation and Motion Curves

  • Chapter 3 of textbook and Appendix B.5

Motion Curves

The most basic capability of an animation to let the user set animation variables in each frame

Not easy to accomplish - HCI challengess in designing effective interface

The next capability is to support key frame animation: Computer automatically interpolating in-between frames

A motion curve is what you get when you plot an animation variable against time (avars)

  • The computer must come up with motion curves that interpolate your keyframe values

  • specify values at certain key frames, work and manipulate curves

Different forms of Curve Functions

Explicit y = f(x) mapping of x to y

  • Cannot get multiple y to same x

Implicit f(x, y) = 0

  • Cannot easily compare tangent vectors at joints
  • In/out test, normals from gradient

Parametric: x = f_x(t), y = f_y(t), z = f_z(t)

  • Most convenient for motion representation

Describing Curves by Means of Polnomials

Lth degree polynomial

p(t) = a_0 + a_1t + a_2t^2 + … + a_Lt^L

a_0 … a_L coefficients

L is degree L+1 is order of polynomial

Parametirc and implicit forms are linie