feat: 增加几何运算辅助函数

CalcRayIsIntersect 根据给定的位置和角度生成射线，检测射线是否与多边形发生碰撞
CalcRadianWithAngle 根据角度 angle 计算弧度
CalcLineSegmentIsIntersect 计算两条线段是否相交
CalcLineSegmentSlope 计算线段的斜率
CalcLineSegmentIntercept 计算线段的截距
ConvertLineSegmentGeneric 转换线段的泛型类型为特定类型
Point.Min 注释为 Max 的问题修复

utils/geometry/circle.go

@@ -8,31 +8,19 @@ import (
 // Circle 圆形
 type Circle[V generic.SignedNumber] struct {
 	Shape[V]
-	radius       V
-	centroid     Point[V]
-	initCentroid bool
 }
 
 // Radius 获取圆形半径
 func (slf Circle[V]) Radius() V {
-	if slf.radius > V(-0) {
-		return slf.radius
-	}
 	for _, point := range slf.Points() {
-		slf.radius = CalcDistanceWithPoint(slf.Centroid(), point)
-		return slf.radius
+		return CalcDistanceWithPoint(slf.Centroid(), point)
 	}
 	panic("circle without any points")
 }
 
 // Centroid 获取圆形质心位置
 func (slf Circle[V]) Centroid() Point[V] {
-	if slf.initCentroid {
-		return slf.centroid
-	}
-	slf.centroid = CalcRectangleCentroid(slf.Shape)
-	slf.initCentroid = true
-	return slf.centroid
+	return CalcRectangleCentroid(slf.Shape)
 }
 
 // Overlap 与另一个圆是否发生重叠

utils/geometry/geometry.go

@@ -133,16 +133,17 @@ func CalcAngle[V generic.SignedNumber](x1, y1, x2, y2 V) V {
 
 // CalcNewCoordinate 根据给定的x、y坐标、角度和距离计算新的坐标
 func CalcNewCoordinate[V generic.SignedNumber](x, y, angle, distance V) (newX, newY V) {
-	// 将角度转换为弧度
+	radian := CalcRadianWithAngle(angle)
+	newX = x + distance*V(math.Cos(float64(radian)))
+	newY = y + distance*V(math.Sin(float64(radian)))
+	return newX, newY
+}
+
+// CalcRadianWithAngle 根据角度 angle 计算弧度
+func CalcRadianWithAngle[V generic.SignedNumber](angle V) V {
 	var pi = math.Pi
 	var dividend = 180.0
-	radians := angle * V(pi) / V(dividend)
-
-	// 计算新的坐标
-	newX = x + distance*V(math.Cos(float64(radians)))
-	newY = y + distance*V(math.Sin(float64(radians)))
-
-	return newX, newY
+	return angle * V(pi) / V(dividend)
 }
 
 // CalcAngleDifference 计算两个角度之间的最小角度差
@@ -155,3 +156,18 @@ func CalcAngleDifference[V generic.SignedNumber](angleA, angleB V) V {
 	t -= V(pi)
 	return t
 }
+
+// CalcRayIsIntersect 根据给定的位置和角度生成射线，检测射线是否与多边形发生碰撞
+func CalcRayIsIntersect[V generic.SignedNumber](x, y, angle V, shape Shape[V]) bool {
+	fx, fy := float64(x), float64(y)
+	radian := CalcRadianWithAngle(float64(angle))
+	end := NewPoint(fx+math.Cos(radian), fy+math.Sin(radian))
+
+	edges := shape.Edges()
+	for i := 0; i < len(edges); i++ {
+		if CalcLineSegmentIsIntersect(NewLineSegment(NewPoint(fx, fy), end), ConvertLineSegmentGeneric[V, float64](edges[i])) {
+			return true
+		}
+	}
+	return false
+}

utils/geometry/line.go

@@ -57,6 +57,13 @@ func (slf LineSegment[V]) GetLength() V {
 	return CalcDistanceWithCoordinate(DoublePointToCoordinate(slf.GetStart(), slf.GetEnd()))
 }
 
+// ConvertLineSegmentGeneric 转换线段的泛型类型为特定类型
+func ConvertLineSegmentGeneric[V generic.SignedNumber, TO generic.SignedNumber](line LineSegment[V]) LineSegment[TO] {
+	x1, y1 := line.GetStart().GetXY()
+	x2, y2 := line.GetEnd().GetXY()
+	return NewLineSegment(NewPoint(TO(x1), TO(y1)), NewPoint(TO(x2), TO(y2)))
+}
+
 // PointOnLineSegmentWithCoordinate 通过一个线段两个点的位置和一个点的坐标，判断这个点是否在一条线段上
 func PointOnLineSegmentWithCoordinate[V generic.SignedNumber](x1, y1, x2, y2, x, y V) bool {
 	return (x-x1)*(y2-y1) == (x2-x1)*(y-y1)
@@ -138,3 +145,37 @@ func CalcLineSegmentIsOverlap[V generic.SignedNumber](line1, line2 LineSegment[V
 	}
 	return NewLineSegment(shapes[1][2].Point, shapes[2][2].Point), true
 }
+
+// CalcLineSegmentIsIntersect 计算两条线段是否相交
+func CalcLineSegmentIsIntersect[V generic.SignedNumber](line1, line2 LineSegment[V]) bool {
+	fl1 := ConvertLineSegmentGeneric[V, float64](line1)
+	fl2 := ConvertLineSegmentGeneric[V, float64](line2)
+	slope1 := CalcLineSegmentSlope(fl1)
+	slope2 := CalcLineSegmentSlope(fl2)
+
+	if slope1 == slope2 {
+		return false
+	}
+
+	intercept1 := CalcLineSegmentIntercept(fl1)
+	intercept2 := CalcLineSegmentIntercept(fl2)
+
+	intersectX := (intercept2 - intercept1) / (slope1 - slope2)
+
+	if intersectX >= maths.Min(fl1.GetStart().GetX(), fl1.GetEnd().GetX()) && intersectX <= maths.Max(fl1.GetStart().GetX(), fl1.GetEnd().GetX()) &&
+		intersectX >= maths.Min(fl2.GetStart().GetX(), fl2.GetEnd().GetX()) && intersectX <= maths.Max(fl2.GetStart().GetX(), fl2.GetEnd().GetX()) {
+		return true
+	}
+
+	return false
+}
+
+// CalcLineSegmentSlope 计算线段的斜率
+func CalcLineSegmentSlope[V generic.SignedNumber](line LineSegment[V]) V {
+	return (line.GetEnd().GetY() - line.GetStart().GetY()) / (line.GetEnd().GetX() - line.GetStart().GetX())
+}
+
+// CalcLineSegmentIntercept 计算线段的截距
+func CalcLineSegmentIntercept[V generic.SignedNumber](line LineSegment[V]) V {
+	return line.GetStart().GetY() - CalcLineSegmentSlope(line)*line.GetStart().GetX()
+}

utils/geometry/line_test.go

@@ -0,0 +1,13 @@
+package geometry_test
+
+import (
+	"fmt"
+	"github.com/kercylan98/minotaur/utils/geometry"
+	"testing"
+)
+
+func TestCalcLineSegmentIsIntersect(t *testing.T) {
+	line1 := geometry.NewLineSegment(geometry.NewPoint(1, 1), geometry.NewPoint(3, 5))
+	line2 := geometry.NewLineSegment(geometry.NewPoint(0, 5), geometry.NewPoint(3, 6))
+	fmt.Println(geometry.CalcLineSegmentIsIntersect(line1, line2))
+}

utils/geometry/position.go

@@ -97,7 +97,7 @@ func (slf Point[V]) Max(point Point[V]) Point[V] {
 	return NewPoint(x, y)
 }
 
-// Max 返回两个位置中每个维度的最小值组成的新的位置
+// Min 返回两个位置中每个维度的最小值组成的新的位置
 func (slf Point[V]) Min(point Point[V]) Point[V] {
 	x, y := slf.GetXY()
 	px, py := point.GetXY()