kercylan98
267 lines
9.8 KiB
Go
267 lines
9.8 KiB
Go
package navmesh
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import (
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"github.com/kercylan98/minotaur/utils/astar"
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"github.com/kercylan98/minotaur/utils/generic"
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"github.com/kercylan98/minotaur/utils/geometry"
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"github.com/kercylan98/minotaur/utils/maths"
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)
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// NewNavMesh 创建一个新的导航网格，并返回一个指向该导航网格的指针。
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//
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// 参数：
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// - shapes: 形状切片，类型为 []geometry.Shape[V]，表示导航网格中的形状。
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// - meshShrinkAmount: 网格缩小量，类型为 V，表示导航网格的缩小量。
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//
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// 返回值：
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// - *NavMesh[V]: 指向创建的导航网格的指针。
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//
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// 注意事项：
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// - 导航网格的形状可以是任何几何形状。
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// - meshShrinkAmount 表示导航网格的缩小量，用于在形状之间创建链接时考虑形状的缩小效果。
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// - 函数内部使用了泛型类型参数 V，可以根据需要指定形状的坐标类型。
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// - 函数返回一个指向创建的导航网格的指针。
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func NewNavMesh[V generic.SignedNumber](shapes []geometry.Shape[V], meshShrinkAmount V) *NavMesh[V] {
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nm := &NavMesh[V]{
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meshShapes: make([]*shape[V], len(shapes)),
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meshShrinkAmount: meshShrinkAmount,
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}
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for i, shape := range shapes {
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nm.meshShapes[i] = newShape(i, shape)
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}
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nm.generateLink()
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return nm
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}
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type NavMesh[V generic.SignedNumber] struct {
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meshShapes []*shape[V]
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meshShrinkAmount V
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}
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// Neighbours 实现 astar.Graph 的接口，用于向 A* 算法提供相邻图形
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func (slf *NavMesh[V]) Neighbours(node *shape[V]) []*shape[V] {
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return node.links
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}
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// Find 用于在 NavMesh 中查找离给定点最近的形状，并返回距离、找到的点和找到的形状。
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//
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// 参数：
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// - point: 给定的点，类型为 geometry.Point[V]，表示一个 V 维度的点坐标。
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// - maxDistance: 最大距离，类型为 V，表示查找的最大距离限制。
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//
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// 返回值：
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// - distance: 距离，类型为 V，表示离给定点最近的形状的距离。
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// - findPoint: 找到的点，类型为 geometry.Point[V]，表示离给定点最近的点坐标。
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// - findShape: 找到的形状，类型为 geometry.Shape[V]，表示离给定点最近的形状。
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//
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// 注意事项：
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// - 如果给定点在 NavMesh 中的某个形状内部或者在形状的边上，距离为 0，找到的形状为该形状，找到的点为给定点。
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// - 如果给定点不在任何形状内部或者形状的边上，将计算给定点到每个形状的距离，并找到最近的形状和对应的点。
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// - 距离的计算采用几何学中的投影点到形状的距离。
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// - 函数返回离给定点最近的形状的距离、找到的点和找到的形状。
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func (slf *NavMesh[V]) Find(point geometry.Point[V], maxDistance V) (distance V, findPoint geometry.Point[V], findShape geometry.Shape[V]) {
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var minDistance = maxDistance
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var closest *shape[V]
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var pointOnClosest geometry.Point[V]
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for _, meshShape := range slf.meshShapes {
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if meshShape.Contains(point) || geometry.IsPointOnEdge(meshShape.Edges(), point) {
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minDistance = 0
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closest = meshShape
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pointOnClosest = point
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break
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}
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br := geometry.CalcBoundingRadius(meshShape.Shape)
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distance := geometry.CalcDistance(geometry.DoublePointToCoordinate(
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geometry.CalcRectangleCentroid(meshShape.Shape),
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point,
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))
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if distance-br < minDistance {
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point, distance := geometry.ProjectionPointToShape(point, meshShape.Shape)
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if distance < minDistance {
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minDistance = distance
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closest = meshShape
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pointOnClosest = point
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}
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}
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}
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return minDistance, pointOnClosest, closest.Shape
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}
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// FindPath 函数用于在 NavMesh 中查找从起点到终点的路径，并返回路径上的点序列。
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//
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// 参数：
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// - start: 起点，类型为 geometry.Point[V]，表示路径的起始点。
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// - end: 终点，类型为 geometry.Point[V]，表示路径的终点。
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//
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// 返回值：
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// - result: 路径上的点序列，类型为 []geometry.Point[V]。
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//
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// 注意事项：
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// - 函数首先根据起点和终点的位置，找到离它们最近的形状作为起点形状和终点形状。
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// - 如果起点或终点不在任何形状内部，且 NavMesh 的 meshShrinkAmount 大于0，则会考虑缩小的形状。
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// - 使用 A* 算法在 NavMesh 上搜索从起点形状到终点形状的最短路径。
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// - 使用漏斗算法对路径进行优化，以得到最终的路径点序列。
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func (slf *NavMesh[V]) FindPath(start, end geometry.Point[V]) (result []geometry.Point[V]) {
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var startShape, endShape *shape[V]
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var startDistance, endDistance = V(-1), V(-1)
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for _, meshShape := range slf.meshShapes {
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br := meshShape.BoundingRadius()
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distance := geometry.CalcDistance(geometry.DoublePointToCoordinate(meshShape.Centroid(), start))
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if (distance <= startDistance || startDistance == V(-1)) && distance <= br && meshShape.Contains(start) {
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startShape = meshShape
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startDistance = distance
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}
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distance = geometry.CalcDistance(geometry.DoublePointToCoordinate(meshShape.Centroid(), end))
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if (distance <= endDistance || endDistance == V(-1)) && distance <= br && meshShape.Contains(end) {
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endShape = meshShape
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endDistance = distance
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}
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}
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if endShape == nil && slf.meshShrinkAmount > V(0) {
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for _, meshShape := range slf.meshShapes {
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br := meshShape.BoundingRadius() + slf.meshShrinkAmount
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distance := geometry.CalcDistance(geometry.DoublePointToCoordinate(meshShape.Centroid(), end))
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if distance <= br {
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_, projectionDistance := geometry.ProjectionPointToShape(end, meshShape.Shape)
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if projectionDistance <= slf.meshShrinkAmount && projectionDistance < endDistance {
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endShape = meshShape
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endDistance = projectionDistance
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}
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}
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}
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}
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if endShape == nil {
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return
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}
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if startShape == nil && slf.meshShrinkAmount > 0 {
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for _, meshShape := range slf.meshShapes {
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br := meshShape.BoundingRadius() + slf.meshShrinkAmount
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distance := geometry.CalcDistance(geometry.DoublePointToCoordinate(meshShape.Centroid(), start))
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if distance <= br {
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_, projectionDistance := geometry.ProjectionPointToShape(start, meshShape.Shape)
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if projectionDistance <= slf.meshShrinkAmount && projectionDistance < startDistance {
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startShape = meshShape
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startDistance = projectionDistance
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}
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}
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}
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}
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if startShape == nil {
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return
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}
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if startShape == endShape {
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return append(result, start, end)
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}
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path := astar.Find[*shape[V], V](slf, startShape, endShape, func(a, b *shape[V]) V {
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return geometry.CalcDistance(geometry.DoublePointToCoordinate(a.centroid, b.centroid))
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}, func(a, b *shape[V]) V {
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return geometry.CalcDistance(geometry.DoublePointToCoordinate(a.centroid, b.centroid))
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})
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if len(path) == 0 {
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return
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}
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path = append([]*shape[V]{startShape}, path...)
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funnel := new(funnel[V])
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funnel.pushSingle(start)
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for i := 0; i < len(path)-1; i++ {
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current := path[i]
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next := path[i+1]
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var portal geometry.Line[V]
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var find bool
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for i := 0; i < len(current.links); i++ {
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if current.links[i].id == next.id {
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portal = current.portals[i]
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find = true
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}
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}
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if !find {
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panic("not found portal")
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}
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funnel.push(portal.GetStart(), portal.GetEnd())
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}
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funnel.pushSingle(end)
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funnel.stringPull()
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var lastPoint geometry.Point[V]
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for i, point := range funnel.path {
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var np = point.Copy()
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if i == 0 || !np.Equal(lastPoint) {
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result = append(result, np)
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}
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lastPoint = np
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}
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return result
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}
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func (slf *NavMesh[V]) generateLink() {
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refer := len(slf.meshShapes)
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for i := 0; i < refer; i++ {
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shapePkg := slf.meshShapes[i]
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shapeCentroid := shapePkg.Centroid()
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shapeBoundingRadius := shapePkg.BoundingRadius()
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shapeEdges := shapePkg.Edges()
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for t := i + 1; t < len(slf.meshShapes); t++ {
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targetShapePkg := slf.meshShapes[t]
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targetShapeCentroid := targetShapePkg.Centroid()
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targetShapeBoundingRadius := targetShapePkg.BoundingRadius()
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centroidDistance := geometry.CalcDistance(geometry.DoublePointToCoordinate(shapeCentroid, targetShapeCentroid))
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if centroidDistance > shapeBoundingRadius+targetShapeBoundingRadius {
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continue
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}
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for _, shapeEdge := range shapeEdges {
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for _, targetEdge := range targetShapePkg.Edges() {
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if !geometry.CalcLineIsCollinear(shapeEdge, targetEdge, V(maths.GetDefaultTolerance())) {
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continue
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}
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var overlapLine, overlap = geometry.CalcLineIsOverlap(shapeEdge, targetEdge)
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if !overlap {
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continue
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}
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shapePkg.links = append(shapePkg.links, targetShapePkg)
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targetShapePkg.links = append(targetShapePkg.links, shapePkg)
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edgeAngle := geometry.CalcAngle(geometry.DoublePointToCoordinate(shapeCentroid, shapeEdge.GetStart()))
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a1 := geometry.CalcAngle(geometry.DoublePointToCoordinate(shapeCentroid, overlapLine.GetStart()))
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a2 := geometry.CalcAngle(geometry.DoublePointToCoordinate(shapeCentroid, overlapLine.GetEnd()))
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a3 := geometry.CalcAngleDifference(edgeAngle, a1)
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a4 := geometry.CalcAngleDifference(edgeAngle, a2)
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if a3 < a4 {
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shapePkg.portals = append(shapePkg.portals, geometry.NewLine(overlapLine.GetStart(), overlapLine.GetEnd()))
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} else {
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shapePkg.portals = append(shapePkg.portals, geometry.NewLine(overlapLine.GetEnd(), overlapLine.GetStart()))
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}
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edgeAngle = geometry.CalcAngle(geometry.DoublePointToCoordinate(targetShapeCentroid, targetEdge.GetStart()))
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a1 = geometry.CalcAngle(geometry.DoublePointToCoordinate(targetShapeCentroid, overlapLine.GetStart()))
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a2 = geometry.CalcAngle(geometry.DoublePointToCoordinate(targetShapeCentroid, overlapLine.GetEnd()))
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a3 = geometry.CalcAngleDifference(edgeAngle, a1)
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a4 = geometry.CalcAngleDifference(edgeAngle, a2)
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if a3 < a4 {
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targetShapePkg.portals = append(targetShapePkg.portals, geometry.NewLine(overlapLine.GetStart(), overlapLine.GetEnd()))
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} else {
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targetShapePkg.portals = append(targetShapePkg.portals, geometry.NewLine(overlapLine.GetEnd(), overlapLine.GetStart()))
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}
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}
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}
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}
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}
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}
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