Optimize and add test to Vec2.signedAngle (#16183)

cocos · Sep 5, 2023 · 42ff683 · 42ff683
1 parent db10a26
commit 42ff683
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Showing 2 changed files with 48 additions and 5 deletions.
diff --git a/cocos/core/math/vec2.ts b/cocos/core/math/vec2.ts
@@ -779,11 +779,18 @@ export class Vec2 extends ValueType {
      * @zh 获取当前向量和指定向量之间的有符号弧度。<br/>
      * 有符号弧度的取值范围为 (-PI, PI]，当前向量可以通过逆时针旋转有符号角度与指定向量同向。<br/>
      * @param other specified vector
-     * @return The signed angle between the current vector and the specified vector (in radians); if there is a zero vector in the current vector and the specified vector, 0 is returned.
+     * @return The signed angle between the current vector and the specified vector (in radians);
+     * if there is a zero vector in the current vector and the specified vector, 0 is returned.
      */
     public signAngle (other: Vec2): number {
-        const angle = this.angle(other);
-        return this.cross(other) < 0 ? -angle : angle;
+        // θ = atan(tan(θ))
+        //   = atan(sin(θ) / cos(θ))
+        //   = atan2(sin(θ), cos(θ))
+        //   = atan2(|a|·|b|·sin(θ), |a|·|b|·cos(θ))
+        //   = atan2(cross(a, b), dot(a, b))
+        const cross = this.cross(other);
+        const dot = this.dot(other);
+        return Math.atan2(cross, dot);
     }
 
     /**

diff --git a/tests/core/math/vec2.test.ts b/tests/core/math/vec2.test.ts
@@ -1,8 +1,9 @@
 import { log } from '../../test.log';
-import { Vec2 } from '../../../cocos/core/math/vec2';
+import { v2, Vec2 } from '../../../cocos/core/math/vec2';
 import { Vec3 } from '../../../cocos/core/math/vec3';
 import { Mat3 } from '../../../cocos/core/math/mat3';
 import { Mat4 } from '../../../cocos/core/math/mat4';
+import { toRadian, toDegree } from '../../../exports/base';
 
 describe('Test Vec2', () => {
     test('normalize', () => {
@@ -71,4 +72,39 @@ describe('Test Vec2', () => {
         log('rotate: ', v0);
         expect(Vec2.equals(v0, expect0)).toBe(true);
     });
-});
+
+    test(`Signed angle`, () => {
+        const t = (v1: Readonly<Vec2>, v2: Readonly<Vec2>, expectedDeg: number) => {
+            expect(toDegree(v1.signAngle(v2))).toBeCloseTo(expectedDeg, 1e-6);
+            expect(toDegree(v2.signAngle(v1))).toBeCloseTo(-expectedDeg, 1e-6);
+        };
+
+        t(v2(0, 0), v2(0, 0), 0.0);
+        t(v2(0, 0), v2(3, -4), 0.0);
+
+        {
+            const v1 = polar(toRadian(10), 2);
+            const v1Angle = 10;
+            const v2 = (deg: number) => polar(toRadian(deg), 0.1);
+
+            t(v1, v2(72.3), 62.3);
+            t(v1, v2(v1Angle + 90), 90);
+            t(v1, v2(v1Angle + 140), 140);
+            t(v1, v2(v1Angle + 179.9999), 179.9999);
+
+            // Opposite vector results singularity.
+            const v2_180 = v2(v1Angle + 180);
+            expect(Math.abs(v1.signAngle(v2_180))).toBeCloseTo(Math.PI);
+            expect(Math.abs(v2_180.signAngle(v1))).toBeCloseTo(Math.PI);
+
+            t(v1, v2(v1Angle + 180.0001), 180.0001 - 360);
+            t(v1, v2(v1Angle + 225), 225 - 360);
+            t(v1, v2(v1Angle + 279.9999), 279.9999 - 360);
+            t(v1, v2(v1Angle + 280.0001), 280.0001 - 360);
+        }
+    });
+});
+
+function polar(angle: number, length: number) {
+    return v2(Math.cos(angle) * length, Math.sin(angle) * length);
+}