add frustumReverseZ

Author: greggman

src/mat4-impl.ts

@@ -789,7 +789,7 @@ export function perspective(fieldOfViewYInRadians: number, aspect: number, zNear
 }
 
 /**
- * Computes a 4-by-4 perspective transformation matrix given the angular height
+ * Computes a 4-by-4 reverse-z 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
@@ -831,13 +831,13 @@ export function perspective(fieldOfViewYInRadians: number, aspect: number, zNear
   dst[13] = 0;
   dst[15] = 0;
 
-  if (Number.isFinite(zFar)) {
+  if (zFar === Infinity) {
+    dst[10] = 0;
+    dst[14] = zNear;
+  } else {
     const rangeInv = 1 / (zFar - zNear);
     dst[10] = zNear * rangeInv;
     dst[14] = zFar * zNear * rangeInv;
-  } else {
-    dst[10] = 0;
-    dst[14] = zNear;
   }
 
   return dst;
@@ -929,6 +929,57 @@ export function frustum(left: number, right: number, bottom: number, top: number
   return dst;
 }
 
+/**
+ * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,
+ * top, bottom, near and far clipping planes. The arguments define a frustum
+ * extending in the negative z direction. 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 (-near) to 0 (-far) in the z
+ * dimension.
+ * @param left - The x coordinate of the left plane of the box.
+ * @param right - The x coordinate of the right plane of the box.
+ * @param bottom - The y coordinate of the bottom plane of the box.
+ * @param top - The y coordinate of the right plane of the box.
+ * @param near - The negative z coordinate of the near plane of the box.
+ * @param far - The negative z coordinate of the far plane of the box.
+ * @param dst - Output matrix. If not passed a new one is created.
+ * @returns The perspective projection matrix.
+ */
+export function frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: Mat4): Mat4 {
+  dst = dst || new MatType(16);
+
+  const dx = (right - left);
+  const dy = (top - bottom);
+
+  dst[ 0] = 2 * near / dx;
+  dst[ 1] = 0;
+  dst[ 2] = 0;
+  dst[ 3] = 0;
+  dst[ 4] = 0;
+  dst[ 5] = 2 * near / dy;
+  dst[ 6] = 0;
+  dst[ 7] = 0;
+  dst[ 8] = (left + right) / dx;
+  dst[ 9] = (top + bottom) / dy;
+  dst[11] = -1;
+  dst[12] = 0;
+  dst[13] = 0;
+  dst[15] = 0;
+
+  if (far === Infinity) {
+    dst[10] = 0;
+    dst[14] = near;
+  } else {
+    const rangeInv = 1 / (far - near);
+    dst[10] = near * rangeInv;
+    dst[14] = far * near * rangeInv;
+  }
+
+  return dst;
+}
+
 let xAxis: Vec3;
 let yAxis: Vec3;
 let zAxis: Vec3;

test/tests/mat4-test.js

@@ -659,6 +659,56 @@ function check(Type) {
       assertEqualApproximately(p[2], 1);
     });
 
+    it('should compute frustumReverseZ', () => {
+      const left = 2;
+      const right = 4;
+      const top = 10;
+      const bottom = 30;
+      const near = 15;
+      const far = 25;
+
+      const dx = (right - left);
+      const dy = (top - bottom);
+      const dz = (far - near);
+
+      const expected = [
+        2 * near / dx,
+        0,
+        0,
+        0,
+        0,
+        2 * near / dy,
+        0,
+        0,
+        (left + right) / dx,
+        (top + bottom) / dy,
+        near / dz,
+        -1,
+        0,
+        0,
+        near * far / dz,
+        0,
+      ];
+      testMat4WithAndWithoutDest((dst) => {
+        return mat4.frustumReverseZ(left, right, bottom, top, near, far, dst);
+      }, expected);
+    });
+
+    it('should compute correct frustumReverseZ', () => {
+      const left = -2;
+      const right = 4;
+      const top = 10;
+      const bottom = 30;
+      const near = 15;
+      const far = 25;
+      const m = mat4.frustumReverseZ(left, right, bottom, top, near, far);
+      shouldBeCloseArray(vec3.transformMat4([left, bottom, -near], m), [-1, -1, 1], 0.000001);
+      const centerX = (left + right) * 0.5;
+      const centerY = (top + bottom) * 0.5;
+      assertEqualApproximately(vec3.transformMat4([centerX, centerY, -near], m)[2], 1);
+      assertEqualApproximately(vec3.transformMat4([centerX, centerY, -far], m)[2], 0);
+    });
+
     it('should compute same frustum as perspective', () => {
       const lr = 4;
       const tb = 2;