Add mat4.perspectiveReverseZ

Author: greggman

src/mat4-impl.ts

@@ -776,13 +776,68 @@ export function perspective(fieldOfViewYInRadians: number, aspect: number, zNear
   dst[13] = 0;
   dst[15] = 0;
 
-  if (zFar === Infinity) {
-    dst[10] = -1;
-    dst[14] = -zNear;
-  } else {
+  if (Number.isFinite(zFar)) {
     const rangeInv = 1 / (zNear - zFar);
     dst[10] = zFar * rangeInv;
     dst[14] = zFar * zNear * rangeInv;
+  } else {
+    dst[10] = -1;
+    dst[14] = -zNear;
+  }
+
+  return dst;
+}
+
+/**
+ * Computes a 4-by-4 perspective transformation matrix given the angular height
+ * of the frustum, the aspect ratio, and the near and far clipping planes.  The
+ * arguments define a frustum extending in the negative z direction.  The given
+ * angle is the vertical angle of the frustum, and the horizontal angle is
+ * determined to produce the given aspect ratio.  The arguments near and far are
+ * the distances to the near and far clipping planes.  Note that near and far
+ * are not z coordinates, but rather they are distances along the negative
+ * z-axis.  The matrix generated sends the viewing frustum to the unit box.
+ * We assume a unit box extending from -1 to 1 in the x and y dimensions and
+ * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.
+ *
+ * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).
+ * @param aspect - The aspect ratio width / height.
+ * @param zNear - The depth (negative z coordinate)
+ *     of the near clipping plane.
+ * @param zFar - The depth (negative z coordinate)
+ *     of the far clipping plane. (default = Infinity)
+ * @param dst - matrix to hold result. If not passed a new one is created.
+ * @returns The perspective matrix.
+ */export function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: Mat4) {
+  dst = dst || new MatType(16);
+
+  const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);
+
+  dst[ 0] = f / aspect;
+  dst[ 1] = 0;
+  dst[ 2] = 0;
+  dst[ 3] = 0;
+
+  dst[ 4] = 0;
+  dst[ 5] = f;
+  dst[ 6] = 0;
+  dst[ 7] = 0;
+
+  dst[ 8] = 0;
+  dst[ 9] = 0;
+  dst[11] = -1;
+
+  dst[12] = 0;
+  dst[13] = 0;
+  dst[15] = 0;
+
+  if (Number.isFinite(zFar)) {
+    const rangeInv = 1 / (zFar - zNear);
+    dst[10] = zNear * rangeInv;
+    dst[14] = zFar * zNear * rangeInv;
+  } else {
+    dst[10] = 0;
+    dst[14] = zNear;
   }
 
   return dst;

test/tests/mat4-test.js

@@ -474,6 +474,95 @@ function check(Type) {
       shouldBeCloseArray(vec3.transformMat4([0, 0, zFar], m), [0, 0, Infinity], 0.000001);
     });
 
+    it('should compute perspective reverseZ with zFar', () => {
+      const fov = 2;
+      const aspect = 4;
+      const zNear = 10;
+      const zFar = 20;
+      const f = Math.tan(Math.PI * 0.5 - 0.5 * fov);
+      const rangeInv = 1 / (zFar - zNear);
+      const expected = [
+        f / aspect,
+        0,
+        0,
+        0,
+
+        0,
+        f,
+        0,
+        0,
+
+        0,
+        0,
+        zNear * rangeInv,
+        -1,
+
+        0,
+        0,
+        zFar * zNear * rangeInv,
+        0,
+      ];
+      testMat4WithAndWithoutDest((dst) => {
+        return mat4.perspectiveReverseZ(fov, aspect, zNear, zFar, dst);
+      }, expected);
+    });
+
+    it('should compute correct perspective reverseZ', () => {
+      const fov = Math.PI / 4;
+      const aspect = 2;
+      const zNear = 10;
+      const zFar = 20;
+      const m = mat4.perspectiveReverseZ(fov, aspect, zNear, zFar);
+      shouldBeCloseArray(vec3.transformMat4([0, 0, -zNear], m), [0, 0, 1], 0.000001);
+      shouldBeCloseArray(vec3.transformMat4([0, 0, -15], m), [0, 0, 0.3333333432674408], 0.000001);
+      shouldBeCloseArray(vec3.transformMat4([0, 0, -zFar], m), [0, 0, 0], 0.000001);
+    });
+
+    it('should compute perspective reverseZ with zFar at infinity', () => {
+      const fov = 2;
+      const aspect = 4;
+      const zNear = 10;
+      const zFar = Infinity;
+      const f = Math.tan(Math.PI * 0.5 - 0.5 * fov);
+      const expected = [
+        f / aspect,
+        0,
+        0,
+        0,
+
+        0,
+        f,
+        0,
+        0,
+
+        0,
+        0,
+        0,
+        -1,
+
+        0,
+        0,
+        zNear,
+        0,
+      ];
+      testMat4WithAndWithoutDest((dst) => {
+        return mat4.perspectiveReverseZ(fov, aspect, zNear, zFar, dst);
+      }, expected);
+    });
+
+    it('should compute correct perspective reverseZ with zFar at Infinity', () => {
+      const fov = Math.PI / 4;
+      const aspect = 2;
+      const zNear = 10;
+      const zFar = Infinity;
+      const m = mat4.perspectiveReverseZ(fov, aspect, zNear, zFar);
+      shouldBeCloseArray(vec3.transformMat4([0, 0, -zNear], m), [0, 0, 1], 0.000001);
+      shouldBeCloseArray(vec3.transformMat4([0, 0, -1000], m), [0, 0, 0.009999999776482582], 0.000001);
+      shouldBeCloseArray(vec3.transformMat4([0, 0, -1000000], m), [0, 0, 0.000009999999747378752], 0.000001);
+      shouldBeCloseArray(vec3.transformMat4([0, 0, -1000000000], m), [0, 0, 9.99999993922529e-9], 0.000001);
+      shouldBeCloseArray(vec3.transformMat4([0, 0, -zFar], m), [0, 0, 0], 0.000001);
+    });
+
     it('should compute ortho', () => {
       const left = 2;
       const right = 4;