package my3d; import javafx.scene.paint.Color; public class _math3d { public static class _point { public double x, y; public _point() { x = 0; y = 0; } public _point(double x, double y) { this.x = x; this.y = y; } public _point set(double x, double y) { this.x = x; this.y = y; return this; } } public static class _vector { public double x, y, z; public _vector() { x = 0; y = 0; z = 0; } public _vector(double x, double y, double z) { this.x = x; this.y = y; this.z = z; } public _vector(_vector v) { x = v.x; y = v.y; z = v.z; } public _vector set(double x, double y, double z) { this.x = x; this.y = y; this.z = z; return this; } public _vector set(_vector v) { x = v.x; y = v.y; z = v.z; return this; } } public static class _matrix { _vector x, y, z; public _matrix() { this(1, 0, 0, 0, 1, 0, 0, 0, 1); } private _matrix( double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double zz) { x = new _vector(xx, xy, xz); y = new _vector(yx, yy, yz); z = new _vector(zx, zy, zz); } private _matrix set( double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double zz) { x.x = xx; x.y = xy; x.z = xz; y.x = yx; y.y = yy; y.z = yz; z.x = zx; z.y = zy; z.z = zz; return this; } public _matrix set(_matrix m) { x.x = m.x.x; x.y = m.x.y; x.z = m.x.z; y.x = m.y.x; y.y = m.y.y; y.z = m.y.z; z.x = m.z.x; z.y = m.z.y; z.z = m.z.z; return this; } public static _matrix rot_x(double t, _matrix mo) { mo.set( 1, 0, 0, 0, Math.cos(t), Math.sin(t), 0, -Math.sin(t), Math.cos(t)); return mo; } public static _matrix rot_y(double t, _matrix mo) { mo.set( Math.cos(t), 0, -Math.sin(t), 0, 1, 0, Math.sin(t), 0, Math.cos(t)); return mo; } public static _matrix rot_z(double t, _matrix mo) { mo.set( Math.cos(t), Math.sin(t), 0, -Math.sin(t), Math.cos(t), 0, 0, 0, 1); return mo; } public static _matrix scale(double k, _matrix mo) { return mo.set( k, 0, 0, 0, k, 0, 0, 0, k); } } public static class _transform { public _matrix orientation; public _vector position; public _transform() { this(new _matrix(), new _vector()); } public _transform(_matrix orientation) { this(orientation, new _vector()); } public _transform(_vector position) { this(new _matrix(), position); } public _transform(_matrix orientation, _vector position) { this.orientation = orientation; this.position = position; } /* public _transform set(_transform tf) { orientation.set(tf.orientation); position.set(tf.position); return this; } */ } public static _vector mul(_matrix m, _vector v, _vector vo) { double x = v.x, y = v.y, z = v.z; vo.x = m.x.x * x + m.y.x * y + m.z.x * z; vo.y = m.x.y * x + m.y.y * y + m.z.y * z; vo.z = m.x.z * x + m.y.z * y + m.z.z * z; return vo; } public static _vector mul(_transform tf, _vector v, _vector vo) { _matrix o = tf.orientation; _vector p = tf.position; double x = v.x, y = v.y, z = v.z; vo.x = o.x.x * x + o.y.x * y + o.z.x * z + p.x; vo.y = o.x.y * x + o.y.y * y + o.z.y * z + p.y; vo.z = o.x.z * x + o.y.z * y + o.z.z * z + p.z; return vo; } private static _vector v_buf1 = new _vector(), v_buf2 = new _vector(); public static _matrix mul(_matrix m1, _matrix m2, _matrix mo) { mul(m1, m2.x, v_buf1); mul(m1, m2.y, v_buf2); mul(m1, m2.z, mo.z); mo.x.set(v_buf1); mo.y.set(v_buf2); return mo; } public static _vector add(_vector v1, _vector v2, _vector vo) { vo.x = v1.x + v2.x; vo.y = v1.y + v2.y; vo.z = v1.z + v2.z; return vo; } // 内積・外積 public static _vector sub(_vector v1, _vector v2, _vector vo) { vo.x = v1.x - v2.x; vo.y = v1.y - v2.y; vo.z = v1.z - v2.z; return vo; } public static double dot(_vector v1, _vector v2) { return v1.x * v2.x + v1.y * v2.y + v1.z * v2.z; } public static _vector cross(_vector v1, _vector v2, _vector vo) { double x = v1.y * v2.z - v1.z * v2.y; double y = v1.z * v2.x - v1.x * v2.z; vo.z = v1.x * v2.y - v1.y * v2.x; vo.x = x; vo.y = y; return vo; } // 光源処理 public static _vector mul(_vector v, double k, _vector vo) { vo.x = v.x * k; vo.y = v.y * k; vo.z = v.z * k; return vo; } public static double len(_vector v) { return Math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z); } public static _vector normalize(_vector v, _vector vo) { return mul(v, 1 / len(v), vo); } public static Color mul(Color c, double k) { return new Color( c.getRed() * k, c.getGreen() * k, c.getBlue() * k, 1); } // クリッピング public static _vector lerp(_vector v1, _vector v2, double t1, _vector vo) { double t2 = 1 - t1; vo.x = v1.x * t1 + v2.x * t2; vo.y = v1.y * t1 + v2.y * t2; vo.z = v1.z * t1 + v2.z * t2; return vo; } // 座標の親子関係 public static _transform mul(_transform tf1, _transform tf2, _transform tfo) { mul(tf1, tf2.position, tfo.position); mul(tf1.orientation, tf2.orientation, tfo.orientation); return tfo; } public static _matrix inv(_matrix m, _matrix mo) { return mo.set( m.x.x, m.y.x, m.z.x, m.x.y, m.y.y, m.z.y, m.x.z, m.y.z, m.z.z); } public static _transform inv(_transform tf, _transform tfo) { inv(tf.orientation, tfo.orientation); mul(tfo.orientation, mul(tf.position, -1, tfo.position), tfo.position); return tfo; } // クォータニオン public static class _quaternion { public double w, x, y, z; public _quaternion() { this(1, 0, 0, 0); } private _quaternion(double w, double x, double y, double z) { this.w = w; this.x = x; this.y = y; this.z = z; } private _quaternion set(double w, double x, double y, double z) { this.w = w; this.x = x; this.y = y; this.z = z; return this; } public _quaternion set(_quaternion q) { w = q.w; x = q.x; y = q.y; z = q.z; return this; } public static _quaternion rot_v(_vector v, double t, _quaternion qo) { t /= 2; normalize(v, v_buf1); qo.w = Math.cos(t); qo.x = v_buf1.x * Math.sin(t); qo.y = v_buf1.y * Math.sin(t); qo.z = v_buf1.z * Math.sin(t); return qo; } public _matrix to_matrix(_matrix mo) { double wx, wy, wz, xx, yy, zz, xy, yz, zx; wx = 2 * w * x; wy = 2 * w * y; wz = 2 * w * z; xx = 2 * x * x; yy = 2 * y * y; zz = 2 * z * z; xy = 2 * x * y; yz = 2 * y * z; zx = 2 * z * x; return mo.set( 1 - yy - zz, xy + wz, zx - wy, xy - wz, 1 - zz - xx, yz + wx, zx + wy, yz - wx, 1 - xx - yy); } public static _quaternion rot_x(double t, _quaternion qo) { t /= 2; return qo.set(Math.cos(t), Math.sin(t), 0, 0); } public static _quaternion rot_y(double t, _quaternion qo) { t /= 2; return qo.set(Math.cos(t), 0, Math.sin(t), 0); } public static _quaternion rot_z(double t, _quaternion qo) { t /= 2; return qo.set(Math.cos(t), 0, 0, Math.sin(t)); } private static _quaternion q_buf1 = new _quaternion(), q_buf2 = new _quaternion(); public static _quaternion euler(double tx, double ty, double tz, _quaternion qo) { return _math3d.mul( _quaternion.rot_y(ty, qo), _math3d.mul( _quaternion.rot_x(tx, q_buf1), _quaternion.rot_z(tz, q_buf2), q_buf2), qo); } } public static _quaternion mul(_quaternion q1, _quaternion q2, _quaternion qo) { double w, x, y; w = q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z; x = q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y; y = q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z; qo.z = q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x; qo.w = w; qo.x = x; qo.y = y; return qo; } public static double dot(_quaternion q1, _quaternion q2) { return q1.w * q2.w + q1.x * q2.x + q1.y * q2.y + q1.z * q2.z; } public static _quaternion slerp(_quaternion q1, _quaternion q2, double t, _quaternion qo) { double w = Math.acos(dot(q1, q2)), sin_w = Math.sin(w); if (Math.abs(sin_w) < 1.0e-3) return q1; double t1 = Math.sin(t * w) / sin_w; double t2 = Math.sin((1 - t) * w) / sin_w; qo.w = q1.w * t2 + q2.w * t1; qo.x = q1.x * t2 + q2.x * t1; qo.y = q1.y * t2 + q2.y * t1; qo.z = q1.z * t2 + q2.z * t1; return qo; } // Zバッファ法 public static int to_argb(Color color) { return 0xff000000 | ((int)(color.getRed() * 255) << 16) | ((int)(color.getGreen() * 255) << 8) | ((int)(color.getBlue() * 255)); } public static int mul(int c, int k) { c = ((c & 0xff0000) * k) & 0xff000000 | ((c & 0xff00) * k) & 0xff0000 | ((c & 0xff) * k) & 0xff00; return 0xff000000 | (c >> 8); } // スムーズ・シェーディング public static int mul_add(int c, int diffuse, int speculer) { int r, g, b; r = ((c & 0xff0000) * diffuse >>> 24) + speculer; g = ((c & 0xff00) * diffuse >>> 16) + speculer; b = ((c & 0xff) * diffuse >>> 8) + speculer; return (0xff000000) | (Math.min(r, 0xff) << 16) | (Math.min(g, 0xff) << 8) | (Math.min(b, 0xff)); } public static _point lerp( _point p1, _point p2, double t1, _point po) { double t2 = 1 - t1; po.x = p1.x * t1 + p2.x * t2; po.y = p1.y * t1 + p2.y * t2; return po; } public static _point lerp( _point p1, _point p2, _point p3, double t1, double t2, double t3, _point po) { po.x = p1.x * t1 + p2.x * t2 + p3.x * t3; po.y = p1.y * t1 + p2.y * t2 + p3.y * t3; return po; } public static _point lerp( _point p1, _point p2, _point p3, _point p4, double t1, double t2, double t3, _point po) { if (t1 > (1 - 10e-3)) return lerp(p1, p4, 0.5, po); lerp(p1, p4, t2 / (1 - t1), po); return lerp(po, p2, p3, t1, t2, t3, po); } public static _vector lerp( _vector v1, _vector v2, double t1, double t2, _vector vo) { vo.x = v1.x * t1 + v2.x * t2; vo.y = v1.y * t1 + v2.y * t2; vo.z = v1.z * t1 + v2.z * t2; return vo; } public static _vector lerp( _vector v1, _vector v2, _vector v3, double t1, double t2, double t3, _vector vo) { vo.x = v1.x * t1 + v2.x * t2 + v3.x * t3; vo.y = v1.y * t1 + v2.y * t2 + v3.y * t3; vo.z = v1.z * t1 + v2.z * t2 + v3.z * t3; return vo; } // テクスチャ public static int add(int c1, int c2) { int t1 = c2 >>> 24; if (t1 == 0xff) return c2; else if (t1 == 0) return c1; int t2 = 0xff - t1; int c = ((c1 & 0xff0000) * t2 + (c2 & 0xff0000) * t1) & 0xff000000 | ((c1 & 0xff00) * t2 + (c2 & 0xff00) * t1) & 0xff0000 | ((c1 & 0xff) * t2 + (c2 & 0xff) * t1) & 0xff00; return 0xff000000 | (c >>> 8); } }