package canvas

import (
	"image"
	"math"
)

// 变换点坐标
func (c *Context) transformPoint(x, y float64) image.Point {
	// 应用变换矩阵 [a, b, c, d, e, f]
	// | a c e |   | x |
	// | b d f | * | y |
	// | 0 0 1 |   | 1 |
	tx := x*c.state.transform[0] + y*c.state.transform[2] + c.state.transform[4]
	ty := x*c.state.transform[1] + y*c.state.transform[3] + c.state.transform[5]
	return image.Point{X: int(tx), Y: int(ty)}
}

// 计算两点之间的距离
func distance(x1, y1, x2, y2 float64) float64 {
	dx := x2 - x1
	dy := y2 - y1
	return math.Sqrt(dx*dx + dy*dy)
}

// 计算贝塞尔曲线点
func bezierPoint(t float64, p0, p1, p2, p3 float64) float64 {
	u := 1 - t
	tt := t * t
	uu := u * u
	uuu := uu * u
	ttt := tt * t

	// (1-t)^3 * P0 + 3 * (1-t)^2 * t * P1 + 3 * (1-t) * t^2 * P2 + t^3 * P3
	return uuu*p0 + 3*uu*t*p1 + 3*u*tt*p2 + ttt*p3
}

// 计算二次贝塞尔曲线点
func quadraticPoint(t float64, p0, p1, p2 float64) float64 {
	u := 1 - t
	return u*u*p0 + 2*u*t*p1 + t*t*p2
}

// 计算椭圆上的点
func ellipsePoint(cx, cy, rx, ry, angle float64) (float64, float64) {
	x := cx + rx*math.Cos(angle)
	y := cy + ry*math.Sin(angle)
	return x, y
}

// 计算圆上的点
func circlePoint(cx, cy, r, angle float64) (float64, float64) {
	return ellipsePoint(cx, cy, r, r, angle)
}