feat(渲染编辑): 修复保存、文字与渲染问题

ofdgo_geom_arc.go

@@ -19,10 +19,19 @@ import (
 	"math"
 )
 
+// geometryArc 保存中心式椭圆及有向参数区间
+type geometryArc struct {
+	center, u, v Point
+	theta, delta float64
+}
+
 // Curves 按毫米误差上限将端点式椭圆弧转换为三次贝塞尔曲线，其他指令保持原样
 // 入参: tolerance 正有限误差上限
 // 返回: GeometryPath 独立路径, error 参数错误
 func (p GeometryPath) Curves(tolerance float64) (GeometryPath, error) {
+	if err := p.validate(); err != nil {
+		return nil, err
+	}
 	if !rasterPositive(tolerance) {
 		return nil, fmt.Errorf("invalid curve tolerance")
 	}
@@ -58,17 +67,53 @@ func (p GeometryPath) Curves(tolerance float64) (GeometryPath, error) {
 // 入参: start 起点, arc 弧线, tolerance 毫米误差上限
 // 返回: GeometryPath 贝塞尔片段, error 无效弧线
 func arcCurves(start Point, arc GeometrySegment, tolerance float64) (GeometryPath, error) {
-	rx, ry := arc.RadiusX, arc.RadiusY
-	if !finite(rx) || !finite(ry) || rx < 0 || ry < 0 || !finite(arc.Rotation) ||
-		!finite(start.X) || !finite(start.Y) || !finite(arc.End.X) || !finite(arc.End.Y) {
-		return nil, fmt.Errorf("invalid arc parameters")
+	a, err := centerArc(start, arc)
+	if err != nil {
+		return nil, err
 	}
 	if start == arc.End {
 		return nil, nil
 	}
-	if rx == 0 || ry == 0 {
+	if arc.RadiusX == 0 || arc.RadiusY == 0 {
 		return GeometryPath{{Verb: GeometryLine, End: arc.End}}, nil
 	}
+	radius := math.Max(math.Hypot(a.u.X, a.u.Y), math.Hypot(a.v.X, a.v.Y))
+	step := math.Min(math.Pi/2, math.Pow(tolerance/radius*40000, 1.0/6))
+	n := math.Ceil(math.Abs(a.delta) / step)
+	if !finite(n) || n < 1 || n > 1<<18 {
+		return nil, fmt.Errorf("arc subdivision limit exceeded")
+	}
+	count := int(n)
+	step = a.delta / float64(count)
+	point := func(x, y float64) Point {
+		return Point{a.center.X + a.u.X*x + a.v.X*y, a.center.Y + a.u.Y*x + a.v.Y*y}
+	}
+	result := make(GeometryPath, 0, count)
+	for i := 0; i < count; i++ {
+		sa, ca := math.Sincos(a.theta + float64(i)*step)
+		sb, cb := math.Sincos(a.theta + float64(i+1)*step)
+		k := 4.0 / 3 * math.Tan(step/4)
+		result = append(result, GeometrySegment{Verb: GeometryCubic, Control1: point(ca-k*sa, sa+k*ca), Control2: point(cb+k*sb, sb-k*cb), End: point(cb, sb)})
+	}
+	result[len(result)-1].End = arc.End
+	return result, nil
+}
+
+// centerArc 将端点式圆弧解析为中心式，统一半径修正和方向语义
+// 入参: start 起点, arc 弧线
+// 返回: geometryArc 中心式参数, error 无效参数或数值溢出
+func centerArc(start Point, arc GeometrySegment) (geometryArc, error) {
+	rx, ry := arc.RadiusX, arc.RadiusY
+	if !finite(rx) || !finite(ry) || rx < 0 || ry < 0 || !finite(arc.Rotation) ||
+		!finite(start.X) || !finite(start.Y) || !finite(arc.End.X) || !finite(arc.End.Y) {
+		return geometryArc{}, fmt.Errorf("invalid arc parameters")
+	}
+	if start == arc.End {
+		return geometryArc{}, nil
+	}
+	if rx == 0 || ry == 0 {
+		return geometryArc{}, nil
+	}
 	angle := math.Mod(arc.Rotation, 360) * math.Pi / 180
 	sine, cosine := math.Sincos(angle)
 	dx, dy := (start.X-arc.End.X)/2, (start.Y-arc.End.Y)/2
@@ -95,23 +140,29 @@ func arcCurves(start Point, arc GeometrySegment, tolerance float64) (GeometryPat
 		delta -= 2 * math.Pi
 	}
 	center := Point{cosine*cx - sine*cy + (start.X+arc.End.X)/2, sine*cx + cosine*cy + (start.Y+arc.End.Y)/2}
-	step := math.Min(math.Pi/2, math.Pow(tolerance/math.Max(rx, ry)*40000, 1.0/6))
-	count := int(math.Ceil(math.Abs(delta) / step))
-	if count < 1 || !finite(center.X) || !finite(center.Y) {
-		return nil, fmt.Errorf("invalid arc extent")
+	if !finite(center.X) || !finite(center.Y) || !finite(rx) || !finite(ry) || !finite(delta) || !finite(theta) || delta == 0 {
+		return geometryArc{}, fmt.Errorf("invalid arc extent")
 	}
-	step = delta / float64(count)
-	point := func(x, y float64) Point {
-		return Point{center.X + rx*cosine*x - ry*sine*y, center.Y + rx*sine*x + ry*cosine*y}
+	return geometryArc{center, Point{rx * cosine, rx * sine}, Point{-ry * sine, ry * cosine}, theta, delta}, nil
+}
+
+// point 计算椭圆参数对应的坐标
+// 入参: angle 参数角
+// 返回: Point 椭圆上的点
+func (a geometryArc) point(angle float64) Point {
+	s, c := math.Sincos(angle)
+	return Point{a.center.X + a.u.X*c + a.v.X*s, a.center.Y + a.u.Y*c + a.v.Y*s}
+}
+
+// fraction 判断参数角是否位于有向弧段内
+// 入参: angle 参数角
+// 返回: float64 弧段比例
+func (a geometryArc) fraction(angle float64) float64 {
+	d := math.Mod(angle-a.theta, 2*math.Pi)
+	if a.delta > 0 && d < 0 {
+		d += 2 * math.Pi
+	} else if a.delta < 0 && d > 0 {
+		d -= 2 * math.Pi
 	}
-	result := make(GeometryPath, 0, count)
-	for i := 0; i < count; i++ {
-		a, b := theta+float64(i)*step, theta+float64(i+1)*step
-		sa, ca := math.Sincos(a)
-		sb, cb := math.Sincos(b)
-		k := 4.0 / 3 * math.Tan(step/4)
-		result = append(result, GeometrySegment{Verb: GeometryCubic, Control1: point(ca-k*sa, sa+k*ca), Control2: point(cb+k*sb, sb-k*cb), End: point(cb, sb)})
-	}
-	result[len(result)-1].End = arc.End
-	return result, nil
+	return d / a.delta
 }