BilinearPatch Class

A bilinear patch is a surface defined by its 4 corner points.

• The corner points do not have to be coplanar, but if they are, the quadrilateral should be convex to avoid a self-intersecting surface.

  $\begin{matrix}
  v\text{-direction}\\
  \uparrow\\
  \text{point01} &\cdots &\text{A1} &\cdots &\text{point11}\\
  \vdots &&\vdots &&\vdots\\
  \text{B0} &\cdots &\text{X} &\cdots &\text{B1}\\
  \vdots &&\vdots &&\vdots\\
  \text{point00} &\cdots &\text{A0} &\cdots &\text{point10} &\rightarrow~u\text{-direction}
  \end{matrix}$

• To evaluate the point at (u,v), the following are equivalent:
  • interpolate first with u then with v:
    • A0 = interpolate between point00 and point10 at fraction u
    • A1 = interpolate between point01 and point11 at fraction u
    • X = interpolate between A0 and A1 at fraction v
  • interpolate first with v then with u:
    • B0 = interpolate between point00 and point01 at fraction v
    • B1 = interpolate between point10 and point11 at fraction v
    • X = interpolate between B0 and B1 at fraction u
  • sum all at once:
    • X = (1-u)(1-v)point00 + (1-u)(v)point01 + (u)(1-v)point10 + (u)(v)point11

Implements

• UVSurface

Methods

Properties

Defined in

• geometry3d/BilinearPatch.ts Line 51