✨ 增加圆形相关处理函数

component/components/moving2d.go

@@ -123,7 +123,7 @@ func (slf *Moving2D) handle() {
 			if interval == 0 {
 				continue
 			}
-			distance := geometry.CalcDistance(x, y, entity.x, entity.y)
+			distance := geometry.CalcDistanceWithCoordinate(x, y, entity.x, entity.y)
 			moveDistance := interval * (entity.GetSpeed() / (slf.timeUnit / 1000 / 1000))
 			if moveDistance >= distance || (x == entity.x && y == entity.y) {
 				entity.SetPosition(entity.x, entity.y)

game/builtin/aoi2d.go

@@ -177,7 +177,7 @@ func (slf *AOI2D) refresh(entity game.AOIEntity2D) {
 	focus := slf.focus[guid]
 	for eg, e := range focus {
 		ex, ey := e.GetPosition()
-		if geometry.CalcDistance(x, y, ex, ey) > vision {
+		if geometry.CalcDistanceWithCoordinate(x, y, ex, ey) > vision {
 			delete(focus, eg)
 			delete(slf.focus[eg], guid)
 		}
@@ -243,13 +243,13 @@ func (slf *AOI2D) rangeVisionAreaEntities(entity game.AOIEntity2D, handle func(g
 			} else {
 				areaY = y
 			}
-			areaDistance := geometry.CalcDistance(x, y, areaX, areaY)
+			areaDistance := geometry.CalcDistanceWithCoordinate(x, y, areaX, areaY)
 			if areaDistance <= vision {
 				for eg, e := range slf.areas[w][h] {
 					if eg == guid {
 						continue
 					}
-					if ex, ey := e.GetPosition(); geometry.CalcDistance(x, y, ex, ey) > vision {
+					if ex, ey := e.GetPosition(); geometry.CalcDistanceWithCoordinate(x, y, ex, ey) > vision {
 						continue
 					}
 					handle(eg, e)

utils/geometry/astar/astar_example_test.go

@@ -37,9 +37,9 @@ func ExampleFind() {
 	}
 
 	paths := astar.Find[geometry.Point[int], int](graph, geometry.NewPoint(1, 1), geometry.NewPoint(8, 6), func(a, b geometry.Point[int]) int {
-		return geometry.CalcDistance(geometry.DoublePointToCoordinate(a, b))
+		return geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(a, b))
 	}, func(a, b geometry.Point[int]) int {
-		return geometry.CalcDistance(geometry.DoublePointToCoordinate(a, b))
+		return geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(a, b))
 	})
 
 	for _, path := range paths {

utils/geometry/circle.go

@@ -5,8 +5,53 @@ import (
 	"math"
 )
 
+// 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
+	}
+	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
+}
+
+// Overlap 与另一个圆是否发生重叠
+func (slf Circle[V]) Overlap(circle Circle[V]) bool {
+	return CalcDistanceWithPoint(slf.Centroid(), circle.Centroid())/2 > slf.radius
+}
+
+// Area 获取圆形面积
+func (slf Circle[V]) Area() V {
+	return V(math.Pi * math.Pow(float64(slf.Radius()), 2))
+}
+
+// Length 获取圆的周长
+func (slf Circle[V]) Length() V {
+	return V(2 * math.Pi * float64(slf.Radius()))
+}
+
 // GenerateCircle 通过传入圆的半径和需要的点数量，生成一个圆
-func GenerateCircle[V generic.SignedNumber](radius V, points int) Shape[V] {
+func GenerateCircle[V generic.SignedNumber](radius V, points int) Circle[V] {
 	angle := 2.0 * math.Pi / float64(points)
 	var shape = make(Shape[V], points)
 	for i := 0; i < points; i++ {
@@ -15,5 +60,5 @@ func GenerateCircle[V generic.SignedNumber](radius V, points int) Shape[V] {
 		y := radius * V(math.Sin(curAngle))
 		shape = append(shape, NewPoint(x, y))
 	}
-	return shape
+	return shape.ToCircle()
 }

utils/geometry/geometry.go

@@ -109,11 +109,16 @@ func CalcDirection[V generic.SignedNumber](x1, y1, x2, y2 V) Direction {
 	return DirectionUnknown
 }
 
-// CalcDistance 计算两点之间的距离
+// CalcDistanceWithCoordinate 计算两点之间的距离
-func CalcDistance[V generic.SignedNumber](x1, y1, x2, y2 V) V {
+func CalcDistanceWithCoordinate[V generic.SignedNumber](x1, y1, x2, y2 V) V {
 	return V(math.Sqrt(math.Pow(float64(x2-x1), 2) + math.Pow(float64(y2-y1), 2)))
 }
 
+// CalcDistanceWithPoint 计算两点之间的距离
+func CalcDistanceWithPoint[V generic.SignedNumber](point1, point2 Point[V]) V {
+	return CalcDistanceWithCoordinate(DoublePointToCoordinate(point1, point2))
+}
+
 // CalcDistanceSquared 计算两点之间的平方距离
 //   - 这个函数的主要用途是在需要计算两点之间距离的情况下，但不需要得到实际的距离值，而只需要比较距离大小。因为平方根运算相对较为耗时，所以在只需要比较大小的情况下，通常会使用平方距离。
 func CalcDistanceSquared[V generic.SignedNumber](x1, y1, x2, y2 V) V {

utils/geometry/line.go

@@ -54,7 +54,7 @@ func (slf LineSegment[V]) GetEnd() Point[V] {
 
 // GetLength 获取该线段的长度
 func (slf LineSegment[V]) GetLength() V {
-	return CalcDistance(DoublePointToCoordinate(slf.GetStart(), slf.GetEnd()))
+	return CalcDistanceWithCoordinate(DoublePointToCoordinate(slf.GetStart(), slf.GetEnd()))
 }
 
 // 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

utils/geometry/navmesh/navmesh.go

@@ -74,7 +74,7 @@ func (slf *NavMesh[V]) Find(point geometry.Point[V], maxDistance V) (distance V,
 			break
 		}
 		br := geometry.CalcBoundingRadius(meshShape.Shape)
-		distance := geometry.CalcDistance(geometry.DoublePointToCoordinate(
+		distance := geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(
 			geometry.CalcRectangleCentroid(meshShape.Shape),
 			point,
 		))
@@ -111,13 +111,13 @@ func (slf *NavMesh[V]) FindPath(start, end geometry.Point[V]) (result []geometry
 	for _, meshShape := range slf.meshShapes {
 		br := meshShape.BoundingRadius()
 
-		distance := geometry.CalcDistance(geometry.DoublePointToCoordinate(meshShape.Centroid(), start))
+		distance := geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(meshShape.Centroid(), start))
 		if (distance <= startDistance || startDistance == V(-1)) && distance <= br && meshShape.Contains(start) {
 			startShape = meshShape
 			startDistance = distance
 		}
 
-		distance = geometry.CalcDistance(geometry.DoublePointToCoordinate(meshShape.Centroid(), end))
+		distance = geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(meshShape.Centroid(), end))
 		if (distance <= endDistance || endDistance == V(-1)) && distance <= br && meshShape.Contains(end) {
 			endShape = meshShape
 			endDistance = distance
@@ -127,7 +127,7 @@ func (slf *NavMesh[V]) FindPath(start, end geometry.Point[V]) (result []geometry
 	if endShape == nil && slf.meshShrinkAmount > V(0) {
 		for _, meshShape := range slf.meshShapes {
 			br := meshShape.BoundingRadius() + slf.meshShrinkAmount
-			distance := geometry.CalcDistance(geometry.DoublePointToCoordinate(meshShape.Centroid(), end))
+			distance := geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(meshShape.Centroid(), end))
 			if distance <= br {
 				_, projectionDistance := geometry.ProjectionPointToShape(end, meshShape.Shape)
 				if projectionDistance <= slf.meshShrinkAmount && projectionDistance < endDistance {
@@ -145,7 +145,7 @@ func (slf *NavMesh[V]) FindPath(start, end geometry.Point[V]) (result []geometry
 	if startShape == nil && slf.meshShrinkAmount > 0 {
 		for _, meshShape := range slf.meshShapes {
 			br := meshShape.BoundingRadius() + slf.meshShrinkAmount
-			distance := geometry.CalcDistance(geometry.DoublePointToCoordinate(meshShape.Centroid(), start))
+			distance := geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(meshShape.Centroid(), start))
 			if distance <= br {
 				_, projectionDistance := geometry.ProjectionPointToShape(start, meshShape.Shape)
 				if projectionDistance <= slf.meshShrinkAmount && projectionDistance < startDistance {
@@ -165,9 +165,9 @@ func (slf *NavMesh[V]) FindPath(start, end geometry.Point[V]) (result []geometry
 	}
 
 	path := astar.Find[*shape[V], V](slf, startShape, endShape, func(a, b *shape[V]) V {
-		return geometry.CalcDistance(geometry.DoublePointToCoordinate(a.centroid, b.centroid))
+		return geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(a.centroid, b.centroid))
 	}, func(a, b *shape[V]) V {
-		return geometry.CalcDistance(geometry.DoublePointToCoordinate(a.centroid, b.centroid))
+		return geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(a.centroid, b.centroid))
 	})
 
 	if len(path) == 0 {
@@ -223,7 +223,7 @@ func (slf *NavMesh[V]) generateLink() {
 			targetShapePkg := slf.meshShapes[t]
 			targetShapeCentroid := targetShapePkg.Centroid()
 			targetShapeBoundingRadius := targetShapePkg.BoundingRadius()
-			centroidDistance := geometry.CalcDistance(geometry.DoublePointToCoordinate(shapeCentroid, targetShapeCentroid))
+			centroidDistance := geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(shapeCentroid, targetShapeCentroid))
 			if centroidDistance > shapeBoundingRadius+targetShapeBoundingRadius {
 				continue
 			}

utils/geometry/navmesh/shape.go

@@ -45,5 +45,5 @@ func (slf *shape[V]) IsWall() bool {
 }
 
 func (slf *shape[V]) GetCost(point geometry.Point[V]) V {
-	return geometry.CalcDistance(geometry.DoublePointToCoordinate(slf.Centroid(), point))
+	return geometry.CalcDistanceWithCoordinate(geometry.DoublePointToCoordinate(slf.Centroid(), point))
 }

utils/geometry/position.go

@@ -59,6 +59,26 @@ func (slf Point[V]) Copy() Point[V] {
 	return PointCopy(slf)
 }
 
+// Add 得到加上 point 后的点
+func (slf Point[V]) Add(point Point[V]) Point[V] {
+	return slf.GetOffset(point.GetXY())
+}
+
+// Sub 得到减去 point 后的点
+func (slf Point[V]) Sub(point Point[V]) Point[V] {
+	return NewPoint(slf.GetX()-point.GetX(), slf.GetY()-point.GetY())
+}
+
+// Mul 得到乘以 point 后的点
+func (slf Point[V]) Mul(point Point[V]) Point[V] {
+	return NewPoint(slf.GetX()*point.GetX(), slf.GetY()*point.GetY())
+}
+
+// Div 得到除以 point 后的点
+func (slf Point[V]) Div(point Point[V]) Point[V] {
+	return NewPoint(slf.GetX()/point.GetX(), slf.GetY()/point.GetY())
+}
+
 // NewPointCap 创建一个由 x、y 坐标组成的点，这个点具有一个数据容量
 func NewPointCap[V generic.SignedNumber, D any](x, y V) PointCap[V, D] {
 	return PointCap[V, D]{

utils/geometry/shape.go

@@ -84,6 +84,12 @@ func (slf Shape[V]) Contains(point Point[V]) bool {
 	return inside
 }
 
+// ToCircle 将形状转换为圆形进行处理
+//   - 当形状非圆形时将会产生意外情况
+func (slf Shape[V]) ToCircle() Circle[V] {
+	return Circle[V]{slf}
+}
+
 // String 将该形状转换为可视化的字符串进行返回
 func (slf Shape[V]) String() string {
 	var result string
@@ -412,7 +418,7 @@ func CalcBoundingRadius[V generic.SignedNumber](shape Shape[V]) V {
 	var boundingRadius V
 	var centroid = CalcRectangleCentroid(shape)
 	for _, point := range shape.Points() {
-		distance := CalcDistance(DoublePointToCoordinate(centroid, point))
+		distance := CalcDistanceWithCoordinate(DoublePointToCoordinate(centroid, point))
 		if distance > boundingRadius {
 			boundingRadius = distance
 		}
@@ -424,7 +430,7 @@ func CalcBoundingRadius[V generic.SignedNumber](shape Shape[V]) V {
 func CalcBoundingRadiusWithCentroid[V generic.SignedNumber](shape Shape[V], centroid Point[V]) V {
 	var boundingRadius V
 	for _, point := range shape.Points() {
-		distance := CalcDistance(DoublePointToCoordinate(centroid, point))
+		distance := CalcDistanceWithCoordinate(DoublePointToCoordinate(centroid, point))
 		if distance > boundingRadius {
 			boundingRadius = distance
 		}
@@ -459,7 +465,7 @@ func ProjectionPointToShape[V generic.SignedNumber](point Point[V], shape Shape[
 
 	for _, edge := range shape.Edges() {
 		projectedPoint := CalcProjectionPoint(edge, point)
-		distance := CalcDistance(DoublePointToCoordinate(point, projectedPoint))
+		distance := CalcDistanceWithCoordinate(DoublePointToCoordinate(point, projectedPoint))
 		if !hasClosestProjection || distance < closestDistance {
 			closestDistance = distance
 			closestProjection = projectedPoint