First commit.

framework/Matrix4.js

@@ -0,0 +1,125 @@
+import Vector3 from "./Vector3.js";
+
+export default class Matrix4 {
+
+	static lookAt( eye, target, up ) {
+
+		const zAxis = Vector3.normalize( Vector3.subtract( eye, target ) );
+
+		const xAxis = Vector3.normalize( Vector3.cross( up, zAxis ) );
+		
+		const yAxis = Vector3.cross( zAxis, xAxis );
+
+		return new Float32Array([
+			xAxis.x, yAxis.x, zAxis.x, 0,
+			xAxis.y, yAxis.y, zAxis.y, 0,
+			xAxis.z, yAxis.z, zAxis.z, 0,
+			-Vector3.dot( xAxis, eye ), -Vector3.dot( yAxis, eye ), -Vector3.dot( zAxis, eye ), 1,
+		]);
+	}
+
+	static getColumn( matrix, index ) {
+		const i = index * 4;
+
+		return new Vector3(
+			matrix[ i + 0 ],
+			matrix[ i + 1 ],
+			matrix[ i + 2 ]
+		);
+	}
+
+	static createProjectionMatrix( camera, canvas ) {
+		return Matrix4.perspective(
+			camera.fovRadians,
+			canvas.width / canvas.height,
+			camera.near,
+			camera.far
+		);
+	}
+
+	static invert( m ) {
+		const out = new Float32Array(16);
+
+		const m00 = m[0],  m01 = m[1],  m02 = m[2],  m03 = m[3];
+		const m10 = m[4],  m11 = m[5],  m12 = m[6],  m13 = m[7];
+		const m20 = m[8],  m21 = m[9],  m22 = m[10], m23 = m[11];
+		const m30 = m[12], m31 = m[13], m32 = m[14], m33 = m[15];
+
+		const a0 = m00 * m11 - m01 * m10;
+		const a1 = m00 * m12 - m02 * m10;
+		const a2 = m00 * m13 - m03 * m10;
+		const a3 = m01 * m12 - m02 * m11;
+		const a4 = m01 * m13 - m03 * m11;
+		const a5 = m02 * m13 - m03 * m12;
+
+		const b0 = m20 * m31 - m21 * m30;
+		const b1 = m20 * m32 - m22 * m30;
+		const b2 = m20 * m33 - m23 * m30;
+		const b3 = m21 * m32 - m22 * m31;
+		const b4 = m21 * m33 - m23 * m31;
+		const b5 = m22 * m33 - m23 * m32;
+
+		const det = a0 * b5 - a1 * b4 + a2 * b3 + a3 * b2 - a4 * b1 + a5 * b0;
+
+		if (det === 0) return null;
+
+		const invDet = 1 / det;
+
+		out[0]  = ( m11 * b5 - m12 * b4 + m13 * b3) * invDet;
+		out[1]  = (-m01 * b5 + m02 * b4 - m03 * b3) * invDet;
+		out[2]  = ( m31 * a5 - m32 * a4 + m33 * a3) * invDet;
+		out[3]  = (-m21 * a5 + m22 * a4 - m23 * a3) * invDet;
+
+		out[4]  = (-m10 * b5 + m12 * b2 - m13 * b1) * invDet;
+		out[5]  = ( m00 * b5 - m02 * b2 + m03 * b1) * invDet;
+		out[6]  = (-m30 * a5 + m32 * a2 - m33 * a1) * invDet;
+		out[7]  = ( m20 * a5 - m22 * a2 + m23 * a1) * invDet;
+
+		out[8]  = ( m10 * b4 - m11 * b2 + m13 * b0) * invDet;
+		out[9]  = (-m00 * b4 + m01 * b2 - m03 * b0) * invDet;
+		out[10] = ( m30 * a4 - m31 * a2 + m33 * a0) * invDet;
+		out[11] = (-m20 * a4 + m21 * a2 - m23 * a0) * invDet;
+
+		out[12] = (-m10 * b3 + m11 * b1 - m12 * b0) * invDet;
+		out[13] = ( m00 * b3 - m01 * b1 + m02 * b0) * invDet;
+		out[14] = (-m30 * a3 + m31 * a1 - m32 * a0) * invDet;
+		out[15] = ( m20 * a3 - m21 * a1 + m22 * a0) * invDet;
+
+		return out;
+	}
+
+	static perspective( fovRadians, aspect, near, far ) {
+
+		const f = 1.0 / Math.tan( fovRadians / 2 );
+
+		const nf = 1 / ( near - far );
+
+		return new Float32Array([
+			f / aspect, 0, 0, 0,
+			0, f, 0, 0,
+			0, 0, (far + near) * nf, -1,
+			0, 0, (2 * far * near) * nf, 0,
+		]);
+	}
+
+	static multiply( a, b ) {
+		const out = new Float32Array(16);
+
+		for ( let col = 0; col < 4; col++ ) {
+			for ( let row = 0; row < 4; row++ ) {
+				let sum = 0;
+
+				for ( let k = 0; k < 4; k++ ) {
+					// a is column-major: element at col k, row row => a[k*4 + row]
+					// b is column-major: element at col col, row k => b[col*4 + k]
+					sum += a[k * 4 + row] * b[col * 4 + k];
+				}
+
+				out[col * 4 + row] = sum;
+			}
+		}
+
+		return out;
+	}
+
+}