在进行交点测试时,首先需要检查贝塞尔曲线的方程是否正确,然后使用牛顿法求根。下面是一个示例代码:
function findIntersection(bez, seg) { // ensure curve is defined correctly if (bez.length !== 4) return null;
// solve for t values using newton's method var roots = []; var p = bez[0], c1 = bez[1], c2 = bez[2], q = bez[3]; var A = 3 * (c1 - p), B = 6 * (c2 - c1) - 3 * A, C = 3 * (p - 2 * c1 + c2); var D = -seg[0] * A - seg[1] * B - seg[2] * C; var E = seg[0] * (3 * A * seg[0] + 2 * B * seg[1] + C * seg[2]) + seg[1] * (2 * A * seg[1] + C * seg[2]) + seg[2] * A * seg[2]; var delta = E * E - 4 * D * A * seg[2]; if (delta < 0) return null; if (delta === 0) { var t = -E / (2 * A * seg[2]); if (t >= 0 && t <= 1) { roots.push(t); } } else { var t1 = (-E + Math.sqrt(delta)) / (2 * A * seg[2]); var t2 = (-E - Math.sqrt(delta)) / (2 * A * seg[2]); if (t1 >= 0 && t1 <= 1) { roots.push(t1); } if (t2 >= 0 && t2 <= 1) { roots.push(t2); } }
return roots; }