Volumetric NURBS

examples-testing/changes.patch

@@ -4348,11 +4348,11 @@ index 537d8d5..bfa97ba 100644
  }
 
 diff --git a/examples-testing/examples/webgl_geometry_nurbs.ts b/examples-testing/examples/webgl_geometry_nurbs.ts
-index 8336ef0..d9c564d 100644
+index 6ab8b32..47ab35c 100644
 --- a/examples-testing/examples/webgl_geometry_nurbs.ts
 +++ b/examples-testing/examples/webgl_geometry_nurbs.ts
-@@ -6,10 +6,10 @@ import { NURBSCurve } from 'three/addons/curves/NURBSCurve.js';
- import { NURBSSurface } from 'three/addons/curves/NURBSSurface.js';
+@@ -7,10 +7,10 @@ import { NURBSSurface } from 'three/addons/curves/NURBSSurface.js';
+ import { NURBSVolume } from 'three/addons/curves/NURBSVolume.js';
  import { ParametricGeometry } from 'three/addons/geometries/ParametricGeometry.js';
 
 -let container, stats;
@@ -4365,7 +4365,7 @@ index 8336ef0..d9c564d 100644
 
  let targetRotation = 0;
  let targetRotationOnPointerDown = 0;
-@@ -78,7 +78,7 @@ function init() {
+@@ -79,7 +79,7 @@ function init() {
      group.add(nurbsLine);
 
      const nurbsControlPointsGeometry = new THREE.BufferGeometry();
@@ -4374,16 +4374,45 @@ index 8336ef0..d9c564d 100644
 
      const nurbsControlPointsMaterial = new THREE.LineBasicMaterial({
          color: 0x333333,
-@@ -123,7 +123,7 @@ function init() {
-     map.anisotropy = 16;
-     map.colorSpace = THREE.SRGBColorSpace;
+@@ -124,7 +124,7 @@ function init() {
+         map.anisotropy = 16;
+         map.colorSpace = THREE.SRGBColorSpace;
 
--    function getSurfacePoint(u, v, target) {
-+    function getSurfacePoint(u: number, v: number, target: THREE.Vector3) {
-         return nurbsSurface.getPoint(u, v, target);
-     }
+-        function getSurfacePoint(u, v, target) {
++        function getSurfacePoint(u: number, v: number, target: THREE.Vector3) {
+             return nurbsSurface.getPoint(u, v, target);
+         }
+
+@@ -175,23 +175,23 @@ function init() {
+         // we create evaluation functions for different surfaces with one of the three
+         // parameter values (u, v, w) kept constant and create multiple THREE.Mesh
+         // objects one for each surface
+-        function getSurfacePointFront(u, v, target) {
++        function getSurfacePointFront(u: number, v: number, target: THREE.Vector3) {
+             return nurbsVolume.getPoint(u, v, 0, target);
+         }
+
+-        function getSurfacePointMiddle(u, v, target) {
++        function getSurfacePointMiddle(u: number, v: number, target: THREE.Vector3) {
+             return nurbsVolume.getPoint(u, v, 0.5, target);
+         }
+
+-        function getSurfacePointBack(u, v, target) {
++        function getSurfacePointBack(u: number, v: number, target: THREE.Vector3) {
+             return nurbsVolume.getPoint(u, v, 1, target);
+         }
+
+-        function getSurfacePointTop(u, w, target) {
++        function getSurfacePointTop(u: number, w: number, target: THREE.Vector3) {
+             return nurbsVolume.getPoint(u, 1, w, target);
+         }
+
+-        function getSurfacePointSide(v, w, target) {
++        function getSurfacePointSide(v: number, w: number, target: THREE.Vector3) {
+             return nurbsVolume.getPoint(0, v, w, target);
+         }
 
-@@ -163,7 +163,7 @@ function onWindowResize() {
+@@ -260,7 +260,7 @@ function onWindowResize() {
 
  //
 
@@ -4392,7 +4421,7 @@ index 8336ef0..d9c564d 100644
      if (event.isPrimary === false) return;
 
      pointerXOnPointerDown = event.clientX - windowHalfX;
-@@ -173,7 +173,7 @@ function onPointerDown(event) {
+@@ -270,7 +270,7 @@ function onPointerDown(event) {
      document.addEventListener('pointerup', onPointerUp);
  }
 
@@ -4401,7 +4430,7 @@ index 8336ef0..d9c564d 100644
      if (event.isPrimary === false) return;
 
      pointerX = event.clientX - windowHalfX;
-@@ -181,7 +181,7 @@ function onPointerMove(event) {
+@@ -278,7 +278,7 @@ function onPointerMove(event) {
      targetRotation = targetRotationOnPointerDown + (pointerX - pointerXOnPointerDown) * 0.02;
  }
 

types/three/examples/jsm/Addons.d.ts

@@ -25,6 +25,7 @@ export * from './csm/CSMShader.js';
 export * as Curves from './curves/CurveExtras.js';
 export * from './curves/NURBSCurve.js';
 export * from './curves/NURBSSurface.js';
+export * from './curves/NURBSVolume.js';
 export * as NURBSUtils from './curves/NURBSUtils.js';
 
 export * from './effects/AnaglyphEffect.js';

types/three/examples/jsm/curves/NURBSUtils.d.ts

@@ -1,20 +1,146 @@
 import { Vector3, Vector4 } from '../../../src/Three.js';
 
-export function findSpan(p: number, u: number, U: number[]): number;
-export function calcBasisFunctions(span: number, u: number, p: number, U: number[]): number[];
-export function calcBSplinePoint(p: number, U: number[], P: Vector4[], u: number): Vector4;
-export function calcBasisFunctionDerivatives(span: number, u: number, p: number, n: number, U: number[]): number[][];
-export function calcBSplineDerivatives(p: number, U: number[], P: Vector4[], u: number, nd: number): Vector4[];
+/**
+ * Finds knot vector span.
+ * @param p degree
+ * @param u parametric value
+ * @param U knot vector
+ * @returns the span
+ */
+export function findSpan(p: number, u: number, U: readonly number[]): number;
+
+/**
+ * Calculate basis functions. See The NURBS Book, page 70, algorithm A2.2
+ * @param span span in which u lies
+ * @param u parametric point
+ * @param p degrees
+ * @param U knot vector
+ * @returns array[p+1] with basis function values
+ */
+export function calcBasisFunctions(span: number, u: number, p: number, U: readonly number[]): number[];
+
+/**
+ * Calculate B-Spline curve points. See The NURBS Book, page 82, algorithm A3.1.
+ * @param p degree of B-Spline
+ * @param U knot vector
+ * @param P control points (x, y, z, w)
+ * @param u parametric point
+ * @returns point for given u
+ */
+export function calcBSplinePoint(p: number, U: readonly number[], P: readonly Vector4[], u: number): Vector4;
+
+/**
+ * Calculate basis functions derivatives. See The NURBS Book, page 72, algorithm A2.3.
+ * @param span span in which u lies
+ * @param u parametric point
+ * @param p degree
+ * @param n number of derivatives to calculate
+ * @param U knot vector
+ * @returns array[n+1][p+1] with basis functions derivatives
+ */
+export function calcBasisFunctionDerivatives(
+    span: number,
+    u: number,
+    p: number,
+    n: number,
+    U: readonly number[],
+): number[][];
+
+/**
+ * Calculate derivatives of a B-Spline. See The NURBS Book, page 93, algorithm A3.2.
+ * @param p degree
+ * @param U knot vector
+ * @param P control points
+ * @param u Parametric points
+ * @param nd number of derivatives
+ * @returns array[d+1] with derivatives
+ */
+export function calcBSplineDerivatives(
+    p: number,
+    U: readonly number[],
+    P: readonly Vector4[],
+    u: number,
+    nd: number,
+): Vector4[];
+
+/**
+ * Calculate "K over I"
+ * @returns k!/(i!(k-i)!
+ */
 export function calcKoverI(k: number, i: number): number;
-export function calcRationalCurveDerivatives(Pders: Vector4[]): Vector3[];
-export function calcNURBSDerivatives(p: number, U: number[], P: Vector4[], u: number, nd: number): Vector3[];
+
+/**
+ * Calculate derivatives (0-nd) of rational curve. See The NURBS Book, page 127, algorithm A4.2.
+ * @param Pders result of function calcBSplineDerivatives
+ * @returns array with derivatives for rational curve.
+ */
+export function calcRationalCurveDerivatives(Pders: readonly Vector4[]): Vector3[];
+
+/**
+ * Calculate NURBS curve derivatives. See The NURBS Book, page 127, algorithm A4.2.
+ * @param p degree
+ * @param U knot vector
+ * @param P control points in homogeneous space
+ * @param u parametric points
+ * @param nd number of derivatives
+ * @returns array with derivatives
+ */
+export function calcNURBSDerivatives(
+    p: number,
+    U: readonly number[],
+    P: readonly Vector4[],
+    u: number,
+    nd: number,
+): Vector3[];
+
+/**
+ * Calculate rational B-Spline surface point. See The NURBS Book, page 134, algorithm A4.3.
+ * @param p degree of B-Spline surface
+ * @param q degree of B-Spline surface
+ * @param U knot vector
+ * @param V knot vector
+ * @param P control points (x, y, z, w)
+ * @param u parametric value
+ * @param v parametric value
+ * @param target
+ * @returns point for given (u, v)
+ */
 export function calcSurfacePoint(
     p: number,
     q: number,
-    U: number[],
-    V: number[],
-    P: Vector4[],
+    U: readonly number[],
+    V: readonly number[],
+    P: readonly (readonly Vector4[])[],
+    u: number,
+    v: number,
+    target: Vector3,
+): Vector3;
+
+/**
+ * Calculate rational B-Spline volume point. See The NURBS Book, page 134, algorithm A4.3.
+ * @param p degree of B-Spline volume
+ * @param q degree of B-Spline volume
+ * @param r degree of B-Spline volume
+ * @param U knot vector
+ * @param V knot vector
+ * @param W knot vector
+ * @param P control points (x, y, z, w)
+ * @param u parametric value
+ * @param v parametric value
+ * @param w parametric value
+ * @param target
+ * @returns point for given (u, v, w)
+ */
+export function calcVolumePoint(
+    p: number,
+    q: number,
+    r: number,
+    U: readonly number[],
+    V: readonly number[],
+    W: readonly number[],
+    P: readonly (readonly (readonly Vector4[])[])[],
     u: number,
     v: number,
+    w: number,
     target: Vector3,
 ): Vector3;

types/three/examples/jsm/curves/NURBSVolume.d.ts

@@ -0,0 +1,23 @@
+import { Vector3, Vector4 } from '../../../src/Three.js';
+
+export class NURBSVolume {
+    degree1: number;
+    degree2: number;
+    degree3: number;
+    knots1: readonly number[];
+    knots2: readonly number[];
+    knots3: readonly number[];
+    controlsPoints: Vector4[][][];
+
+    constructor(
+        degree1: number,
+        degree2: number,
+        degree3: number,
+        knots1: readonly number[],
+        knots2: readonly number[],
+        knots3: readonly number[],
+        controlsPoints: Vector4[][][],
+    );
+
+    getPoint(t1: number, t2: number, t3: number, target: Vector3): void;
+}