API Reference › core-geometry › Solid › BilinearPatch

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.
    v-direction↑point01⋯A1⋯point11⋮⋮⋮B0⋯X⋯B1⋮⋮⋮point00⋯A0⋯point10→ u-direction\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

Methods

Name Description
constructor(point00: Point3d, point10: Point3d, point01: Point3d, point11: Point3d): BilinearPatch Capture (not clone) corners to create a new BilinearPatch.  
clone(): BilinearPatch Return a cloned patch.  
cloneTransformed(transform: Transform): undefined | BilinearPatch Return a cloned and transformed patch.  
extendRange(range: Range3d, transform?: Transform): void Extend a range by the range of the (optionally transformed) patch.  
intersectRay(ray: Ray3d): undefined | CurveAndSurfaceLocationDetail[] Compute the points of intersection with a ray.  
isAlmostEqual(other: BilinearPatch): boolean Test equality of the 4 points.  
maxUEdgeLength(): number Returns the larger of the u-direction edge lengths at v=0 and v=1.  
maxVEdgeLength(): number Returns the larger of the v-direction edge lengths at u=0 and u=1.  
tryTransformInPlace(transform: Transform): boolean Apply the transform to each point.  
uvFractionToPoint(u: number, v: number, result?: Point3d): Point3d Convert fractional u and v coordinates to surface point  
uvFractionToPointAndTangents(u: number, v: number, result?: Plane3dByOriginAndVectors): Plane3dByOriginAndVectors Evaluate as a uv surface, returning point and two derivative vectors.  
create(point00: Point3d, point10: Point3d, point01: Point3d, point11: Point3d): BilinearPatch Static Clone (not capture) corners to create a new BilinearPatch.  
createXYZ(x00: number, y00: number, z00: number, x10: number, y10: number, z10: number, x01: number, y01: number, z01: number, x11: number, y11: number, z11: number): BilinearPatch Static Create a patch from xyz values of the 4 corners.  

Properties

Name Type Description
point00 Point3d corner at parametric coordinate (0,0)  
point01 Point3d corner at parametric coordinate (0,1)  
point10 Point3d corner at parametric coordinate (1,0)  
point11 Point3d corner at parametric coordinate (1,1)  

Defined in

Last Updated: 16 April, 2024