mirror of
https://github.com/xiaoqidun/ofdgo.git
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130 lines
3.9 KiB
Go
130 lines
3.9 KiB
Go
// Copyright 2025-2026 肖其顿 (XIAO QI DUN)
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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package geom
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import "math"
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// polygonPoint 允许同结构的后端顶点直接参与裁剪，避免整片坐标转换
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type polygonPoint interface {
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~struct{ X, Y float64 }
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}
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// ClipPolygon 按非退化凸窗口逐边裁剪多边形，保留原顶点绕向，不修改输入
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// 入参: a 绘制顶点, b 已通过ConvexPolygon检查的裁剪顶点，均不含重复闭合点
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// 返回: []P 交集顶点，少于三个顶点时不构成区域, bool 是否满足数值精度
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func ClipPolygon[P polygonPoint](a, b []P) ([]P, bool) {
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for i, start := range b {
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origin, end := Point(start), Point(b[(i+1)%len(b)])
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dx, dy := end.X-origin.X, end.Y-origin.Y
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length := math.Hypot(dx, dy)
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if length == 0 {
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continue
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}
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dx, dy = dx/length, dy/length
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distance := func(p P) float64 { return convexDistance(origin, Point(p), dx, dy) }
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sign := 1.0
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for _, p := range b {
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if d := distance(p); d != 0 {
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sign = math.Copysign(1, d)
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break
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}
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}
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if len(a) == 0 {
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break
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}
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var clipped []P
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appendPoint := func(p P) {
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if len(clipped) == 0 || p != clipped[len(clipped)-1] {
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clipped = append(clipped, p)
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}
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}
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previous := a[len(a)-1]
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previousDistance := sign * distance(previous)
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if !finite(previousDistance) {
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return nil, false
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}
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for _, p := range a {
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d := sign * distance(p)
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if !finite(d) {
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return nil, false
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}
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if (d >= 0) != (previousDistance >= 0) {
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scale := math.Max(math.Abs(d), math.Abs(previousDistance))
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fraction := (previousDistance / scale) / (previousDistance/scale - d/scale)
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intersection := Lerp(Point(previous), Point(p), fraction)
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if dx == 0 {
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intersection.X = origin.X
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}
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if dy == 0 {
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intersection.Y = origin.Y
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}
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appendPoint(P(intersection))
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}
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if d >= 0 {
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appendPoint(p)
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}
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previous, previousDistance = p, d
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}
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if len(clipped) > 1 && clipped[0] == clipped[len(clipped)-1] {
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clipped = clipped[:len(clipped)-1]
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}
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a = clipped
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}
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return a, true
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}
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// ConvexPolygon 检查所有顶点位于各边的同一侧，不修改输入
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// 入参: points 不含重复闭合点的独立顶点
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// 返回: []P 原顶点，非有限距离或异侧顶点返回nil, bool 是否为非退化凸多边形
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func ConvexPolygon[P polygonPoint](points []P) ([]P, bool) {
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positive := false
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for i, start := range points {
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origin, end := Point(start), Point(points[(i+1)%len(points)])
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dx, dy := end.X-origin.X, end.Y-origin.Y
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length := math.Hypot(dx, dy)
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if !finite(length) {
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return nil, false
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}
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if length == 0 {
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continue
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}
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dx, dy = dx/length, dy/length
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sign := 0.0
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for _, p := range points {
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d := convexDistance(origin, Point(p), dx, dy)
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if !finite(d) || sign*d < 0 {
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return nil, false
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}
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if d != 0 {
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sign, positive = math.Copysign(1, d), true
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}
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}
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}
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return points, positive
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}
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// convexDistance 按浮点乘法误差界识别共线点，不使用固定坐标容差
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// 入参: start 边起点, point 待测顶点, dx 横向单位分量, dy 纵向单位分量
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// 返回: float64 顶点到边的有向距离
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func convexDistance(start, point Point, dx, dy float64) float64 {
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x, y := point.X-start.X, point.Y-start.Y
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distance := math.FMA(dx, y, -dy*x)
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errorBound := (math.Abs(dx*y) + math.Abs(dy*x)) * 0x1p-49
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if finite(errorBound) && math.Abs(distance) <= errorBound {
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return 0
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}
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return distance
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}
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