manifold-3d/lib/math.js

Geometry library for topological robustness

// Copyright 2022-2025 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
const { cos, sin, sqrt, PI } = Math;
/**
 * Convert Euler (Tait-Bryan) angles to a quaternion.
 *
 * From the reference frame of the model being rotated, rotations are applied in
 * *z-y'-x"* order. That is yaw first, then pitch and finally roll.
 *
 * From the global reference frame, a model will be rotated in *x-y-z* order.
 * That is about the global X axis, then global Y axis, and finally global Z.
 *
 * This matches the behaviour of `Manifold.rotate()`.
 *
 * @param rotation [X, Y, Z] rotation in degrees.
 */
export function euler2quat(rotation) {
    const [cx, cy, cz] = rotation.map(r => cos(r * PI / 360));
    const [sx, sy, sz] = rotation.map(r => sin(r * PI / 360));
    return [
        sx * cy * cz - cx * sy * sz, // X
        cx * sy * cz + sx * cy * sz, // Y
        cx * cy * sz - sx * sy * cz, // Z
        cx * cy * cz + sx * sy * sz // W
    ];
}
/**
 * Multiply two quaternions together.  This is useful for stacking rotations.
 */
export function multiplyQuat(a, b) {
    const [ax, ay, az, aw] = a;
    const [bx, by, bz, bw] = b;
    return [
        ax * bw + aw * bx + ay * bz - az * by, // X
        ay * bw + aw * by + az * bx - ax * bz, // Y
        az * bw + aw * bz + ax * by - ay * bx, // Z
        aw * bw - ax * bx - ay * by - az * bz // W
    ];
}
/**
 * Calculate the distance between two vectors.
 */
export function distanceVec3(a, b) {
    return sqrt((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2 + (a[2] - b[2]) ** 2);
}
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