#include "bezier_curve.h"

// 三次贝塞尔曲线，二维
void bezier_curve_3rd(const float p0[2], const float p1[2], const float p2[2], const float p3[2], float t, float out[2]) {
    float u = 1.0f - t;
    float tt = t * t;
    float uu = u * u;
    float uuu = uu * u;
    float ttt = tt * t;
    out[0] = uuu * p0[0] + 3 * uu * t * p1[0] + 3 * u * tt * p2[0] + ttt * p3[0];
    out[1] = uuu * p0[1] + 3 * uu * t * p1[1] + 3 * u * tt * p2[1] + ttt * p3[1];
}

// 三次贝塞尔曲线，三维
void bezier_curve_3rd_3d(const float p0[3], const float p1[3], const float p2[3], const float p3[3], float t, float out[3]) {
    float u = 1.0f - t;
    float tt = t * t;
    float uu = u * u;
    float uuu = uu * u;
    float ttt = tt * t;
    for (int i = 0; i < 3; ++i) {
        out[i] = uuu * p0[i] + 3 * uu * t * p1[i] + 3 * u * tt * p2[i] + ttt * p3[i];
    }
}