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Fixed zero tangents

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This commit is contained in:
Alexander Nozik 2023-04-16 20:08:04 +03:00
parent df675c8d45
commit 375de71ca6
3 changed files with 218 additions and 259 deletions
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467
trajectory-kt/src/commonMain/kotlin/space/kscience/kmath/trajectory/Obstacle.kt
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@ -12,6 +12,7 @@ import space.kscience.kmath.geometry.Euclidean2DSpace.norm
import space.kscience.kmath.geometry.Euclidean2DSpace.plus
import space.kscience.kmath.geometry.Euclidean2DSpace.times
import space.kscience.kmath.geometry.Euclidean2DSpace.vector
import space.kscience.kmath.misc.zipWithNextCircular
import space.kscience.kmath.operations.DoubleField.pow
import kotlin.math.*
@ -25,6 +26,14 @@ internal data class Tangent(
val endDirection: Trajectory2D.Direction = startDirection,
) : LineSegment2D by lineSegment
private class LR<T>(val l: T, val r: T) {
operator fun get(direction: Trajectory2D.Direction) = when (direction) {
Trajectory2D.L -> l
Trajectory2D.R -> r
}
}
private class TangentPath(val tangents: List<Tangent>) {
fun last() = tangents.last()
}
@ -35,7 +44,7 @@ private fun TangentPath(vararg tangents: Tangent) = TangentPath(listOf(*tangents
* Create inner and outer tangents between two circles.
* This method returns a map of segments using [DubinsPath] connection type notation.
*/
internal fun tangentsToCircle(
internal fun tangentsBetweenCircles(
first: Circle2D,
second: Circle2D,
): Map<DubinsPath.Type, LineSegment2D> = with(Euclidean2DSpace) {
@ -48,6 +57,7 @@ internal fun tangentsToCircle(
val distance = line.begin.distanceTo(line.end)
val angle1 = atan2(second.center.x - first.center.x, second.center.y - first.center.y)
var angle2: Double
return listOf(
DubinsPath.Type.RSR,
DubinsPath.Type.RSL,
@ -83,192 +93,122 @@ internal fun tangentsToCircle(
)
}
}
//
//private fun dubinsTangentsToCircles(
// firstCircle: Circle2D,
// secondCircle: Circle2D,
// firstObstacle: Obstacle,
// secondObstacle: Obstacle,
//): Map<DubinsPath.Type, Tangent> = with(Euclidean2DSpace) {
// val line = LineSegment(firstCircle.center, secondCircle.center)
// val distance = line.begin.distanceTo(line.end)
// val angle1 = atan2(
// secondCircle.center.x - firstCircle.center.x,
// secondCircle.center.y - firstCircle.center.y
// )
// var r: Double
// var angle2: Double
// val routes = mapOf(
// DubinsPath.Type.RSR to Pair(firstCircle.radius, secondCircle.radius),
// DubinsPath.Type.RSL to Pair(firstCircle.radius, -secondCircle.radius),
// DubinsPath.Type.LSR to Pair(-firstCircle.radius, secondCircle.radius),
// DubinsPath.Type.LSL to Pair(-firstCircle.radius, -secondCircle.radius)
// )
// return buildMap {
// for ((route: DubinsPath.Type, r1r2) in routes) {
// val r1 = r1r2.first
// val r2 = r1r2.second
// r = if (r1.sign == r2.sign) {
// r1.absoluteValue - r2.absoluteValue
// } else {
// r1.absoluteValue + r2.absoluteValue
// }
// if (distance * distance >= r * r) {
// val l = sqrt(distance * distance - r * r)
// angle2 = if (r1.absoluteValue > r2.absoluteValue) {
// angle1 + r1.sign * atan2(r.absoluteValue, l)
// } else {
// angle1 - r2.sign * atan2(r.absoluteValue, l)
// }
// val w = vector(-cos(angle2), sin(angle2))
// put(
// route,
// Tangent(
// startCircle = Circle2D(firstCircle.center, firstCircle.radius),
// endCircle = secondCircle,
// startObstacle = firstObstacle,
// endObstacle = secondObstacle,
// lineSegment = LineSegment(
// firstCircle.center + w * r1,
// secondCircle.center + w * r2
// ),
// startDirection = route.first,
// endDirection = route.third
// )
// )
// } else {
// throw Exception("Circles should not intersect")
// }
// }
// }
//}
internal class Obstacle(
public val circles: List<Circle2D>,
) {
internal val tangents: List<Tangent> = boundaryTangents().first
public val boundaryRoute: DubinsPath.Type = boundaryTangents().second
public val center: Vector2D<Double> = vector(
circles.sumOf { it.center.x } / circles.size,
circles.sumOf { it.center.y } / circles.size
)
private fun boundaryTangents(): Pair<List<Tangent>, DubinsPath.Type> {
internal val tangents: List<LineSegment2D>
public val direction: Trajectory2D.Direction
init {
// outer tangents for a polygon circles can be either lsl or rsr
fun Circle2D.dubinsTangentsToCircles(
other: Circle2D,
): Map<DubinsPath.Type, Tangent> = with(Euclidean2DSpace) {
val line = LineSegment(center, other.center)
val d = line.begin.distanceTo(line.end)
val angle1 = atan2(other.center.x - center.x, other.center.y - center.y)
var r: Double
var angle2: Double
val routes = mapOf(
DubinsPath.Type.RSR to Pair(radius, other.radius),
DubinsPath.Type.LSL to Pair(-radius, -other.radius)
)
return buildMap {
for ((routeType, r1r2) in routes) {
val r1 = r1r2.first
val r2 = r1r2.second
r = if (r1.sign == r2.sign) {
r1.absoluteValue - r2.absoluteValue
} else {
r1.absoluteValue + r2.absoluteValue
}
if (d * d >= r * r) {
val l = (d * d - r * r).pow(0.5)
angle2 = if (r1.absoluteValue > r2.absoluteValue) {
angle1 + r1.sign * atan2(r.absoluteValue, l)
} else {
angle1 - r2.sign * atan2(r.absoluteValue, l)
}
val w = vector(-cos(angle2), sin(angle2))
put(
routeType, Tangent(
Circle2D(center, radius),
other,
this@Obstacle,
this@Obstacle,
LineSegment(
center + w * r1,
other.center + w * r2
),
startDirection = routeType.first,
endDirection = routeType.third
)
)
} else {
throw Exception("Circles should not intersect")
}
}
}
}
val firstCircles = circles
val secondCircles = circles.slice(1..circles.lastIndex) +
circles[0]
val lslTangents = firstCircles.zip(secondCircles)
{ a, b -> a.dubinsTangentsToCircles(b)[DubinsPath.Type.LSL]!! }
val rsrTangents = firstCircles.zip(secondCircles)
{ a, b -> a.dubinsTangentsToCircles(b)[DubinsPath.Type.RSR]!! }
val center = vector(
circles.sumOf { it.center.x } / circles.size,
circles.sumOf { it.center.y } / circles.size
)
val lslToCenter = lslTangents.sumOf { it.lineSegment.begin.distanceTo(center) } +
lslTangents.sumOf { it.lineSegment.end.distanceTo(center) }
val rsrToCenter = rsrTangents.sumOf { it.lineSegment.begin.distanceTo(center) } +
rsrTangents.sumOf { it.lineSegment.end.distanceTo(center) }
return if (rsrToCenter >= lslToCenter) {
Pair(rsrTangents, DubinsPath.Type.RSR)
// fun dubinsTangentsToCircles(
// firstCircle: Circle2D,
// secondCircle: Circle2D,
// ): LR<Tangent> = with(Euclidean2DSpace) {
// val line = LineSegment(firstCircle.center, secondCircle.center)
// val d = line.begin.distanceTo(line.end)
// val angle1 = atan2(secondCircle.center.x - firstCircle.center.x, secondCircle.center.y - firstCircle.center.y)
// var r: Double
// var angle2: Double
// val routes = mapOf(
// Trajectory2D.R to Pair(firstCircle.radius, secondCircle.radius),
// Trajectory2D.L to Pair(-firstCircle.radius, -secondCircle.radius)
// )
// return buildMap {
// for ((routeType, r1r2) in routes) {
// val r1 = r1r2.first
// val r2 = r1r2.second
// r = if (r1.sign == r2.sign) {
// r1.absoluteValue - r2.absoluteValue
// } else {
// r1.absoluteValue + r2.absoluteValue
// }
// if (d * d >= r * r) {
// val l = (d * d - r * r).pow(0.5)
// angle2 = if (r1.absoluteValue > r2.absoluteValue) {
// angle1 + r1.sign * atan2(r.absoluteValue, l)
// } else {
// angle1 - r2.sign * atan2(r.absoluteValue, l)
// }
// val w = this.vector(-cos(angle2), sin(angle2))
// this.put(
// routeType, Tangent(
// Circle2D(firstCircle.center, firstCircle.radius),
// secondCircle,
// this@Obstacle,
// this@Obstacle,
// LineSegment(
// firstCircle.center + w * r1,
// secondCircle.center + w * r2
// ),
// startDirection = routeType.first,
// endDirection = routeType.third
// )
// )
// } else {
// throw Exception("Circles should not intersect")
// }
// }
// }
// }
if (circles.size < 2) {
tangents = emptyList()
direction = Trajectory2D.R
} else {
Pair(lslTangents, DubinsPath.Type.LSL)
val lslTangents = circles.zipWithNextCircular { a, b ->
tangentsBetweenCircles(a, b)[DubinsPath.Type.LSL]!!
}
val rsrTangents = circles.zipWithNextCircular { a, b ->
tangentsBetweenCircles(a, b)[DubinsPath.Type.RSR]!!
}
val center = vector(
circles.sumOf { it.center.x } / circles.size,
circles.sumOf { it.center.y } / circles.size
)
val lslToCenter =
lslTangents.sumOf { it.begin.distanceTo(center) } + lslTangents.sumOf { it.end.distanceTo(center) }
val rsrToCenter =
rsrTangents.sumOf { it.begin.distanceTo(center) } + rsrTangents.sumOf { it.end.distanceTo(center) }
if (rsrToCenter >= lslToCenter) {
this.tangents = rsrTangents
this.direction = Trajectory2D.R
} else {
this.tangents = lslTangents
this.direction = Trajectory2D.L
}
}
}
internal fun nextTangent(circle: Circle2D, direction: Trajectory2D.Direction): Tangent {
if (direction == boundaryRoute.first) {
for (i in circles.indices) {
if (circles[i] == circle) {
return tangents[i]
}
}
val circleIndex = circles.indexOf(circle)
if (circleIndex == -1) error("Circle does not belong to this tangent")
val nextCircleIndex = if (direction == this.direction) {
if (circleIndex == circles.lastIndex) 0 else circleIndex + 1
} else {
for (i in circles.indices) {
if (circles[i] == circle) {
if (i > 0) {
return Tangent(
circles[i],
circles[i - 1],
this,
this,
LineSegment(
tangents[i - 1].lineSegment.end,
tangents[i - 1].lineSegment.begin
),
direction
)
} else {
return Tangent(
circles[0],
circles.last(),
this,
this,
LineSegment(
tangents.last().lineSegment.end,
tangents.last().lineSegment.begin
),
direction
)
}
}
}
if (circleIndex == 0) circles.lastIndex else circleIndex - 1
}
error("next tangent not found")
return Tangent(
circle,
circles[nextCircleIndex],
this,
this,
LineSegment(
tangents[nextCircleIndex].end,
tangents[nextCircleIndex].begin
),
direction
)
}
override fun equals(other: Any?): Boolean {
@ -283,7 +223,7 @@ internal class Obstacle(
internal fun Obstacle(vararg circles: Circle2D): Obstacle = Obstacle(listOf(*circles))
private fun LineSegment2D.intersectSegment(other: LineSegment2D): Boolean {
private fun LineSegment2D.intersectsSegment(other: LineSegment2D): Boolean {
fun crossProduct(v1: DoubleVector2D, v2: DoubleVector2D): Double {
return v1.x * v2.y - v1.y * v2.x
}
@ -299,7 +239,7 @@ private fun LineSegment2D.intersectSegment(other: LineSegment2D): Boolean {
}
}
private fun LineSegment2D.intersectCircle(circle: Circle2D): Boolean {
private fun LineSegment2D.intersectsCircle(circle: Circle2D): Boolean {
val a = (begin.x - end.x).pow(2.0) + (begin.y - end.y).pow(2.0)
val b = 2 * ((begin.x - end.x) * (end.x - circle.center.x) +
(begin.y - end.y) * (end.y - circle.center.y))
@ -318,27 +258,28 @@ private fun LineSegment2D.intersectCircle(circle: Circle2D): Boolean {
return false
}
private fun Tangent.intersectObstacle(obstacle: Obstacle): Boolean {
for (tangent in obstacle.tangents) {
if (lineSegment.intersectSegment(tangent.lineSegment)) {
return true
}
}
for (circle in obstacle.circles) {
if (lineSegment.intersectCircle(circle)) {
return true
}
}
return false
}
/**
* Check if segment has any intersections with an obstacle
*/
private fun LineSegment2D.intersectsObstacle(obstacle: Obstacle): Boolean =
obstacle.tangents.any { tangent -> intersectsSegment(tangent) }
|| obstacle.circles.any { circle -> intersectsCircle(circle) }
/**
* All tangents between two obstacles
*
* In general generates 4 paths.
* TODO check intersections.
*/
private fun outerTangents(first: Obstacle, second: Obstacle): Map<DubinsPath.Type, Tangent> = buildMap {
for (circle1 in first.circles) {
for (circle2 in second.circles) {
for ((pathType, segment) in tangentsToCircle(circle1, circle2)) {
for (firstCircle in first.circles) {
for (secondCircle in second.circles) {
for ((pathType, segment) in tangentsBetweenCircles(firstCircle, secondCircle)) {
val tangent = Tangent(
circle1,
circle2,
firstCircle,
secondCircle,
first,
second,
segment,
@ -346,9 +287,7 @@ private fun outerTangents(first: Obstacle, second: Obstacle): Map<DubinsPath.Typ
pathType.third
)
if (!(tangent.intersectObstacle(first))
and !(tangent.intersectObstacle(second))
) {
if (!(tangent.intersectsObstacle(first)) && !(tangent.intersectsObstacle(second))) {
put(
pathType,
tangent
@ -395,23 +334,24 @@ private fun normalVectors(v: DoubleVector2D, r: Double): Pair<DoubleVector2D, Do
)
}
private fun constructTangentCircles(
point: DoubleVector2D,
direction: DoubleVector2D,
r: Double,
): Map<Trajectory2D.Type, Circle2D> {
): LR<Circle2D> {
val center1 = point + normalVectors(direction, r).first
val center2 = point + normalVectors(direction, r).second
val p1 = center1 - point
return if (atan2(p1.y, p1.x) - atan2(direction.y, direction.x) in listOf(PI / 2, -3 * PI / 2)) {
mapOf(
Trajectory2D.L to Circle2D(center1, r),
Trajectory2D.R to Circle2D(center2, r)
LR(
Circle2D(center1, r),
Circle2D(center2, r)
)
} else {
mapOf(
Trajectory2D.L to Circle2D(center2, r),
Trajectory2D.R to Circle2D(center1, r)
LR(
Circle2D(center2, r),
Circle2D(center1, r)
)
}
}
@ -439,6 +379,9 @@ private fun tangentsAlongTheObstacle(
return dubinsTangents
}
/**
* Check if all proposed paths have ended at [finalObstacle]
*/
private fun allFinished(
paths: List<TangentPath>,
finalObstacle: Obstacle,
@ -481,92 +424,114 @@ internal fun findAllPaths(
): List<CompositeTrajectory2D> {
fun DubinsPose2D.direction() = vector(cos(bearing), sin(bearing))
// two circles for the initial point
val initialCircles = constructTangentCircles(
start,
start.direction(),
startingRadius
)
//two circles for the final point
val finalCircles = constructTangentCircles(
finish,
finish.direction(),
finalRadius
)
//all valid trajectories
val trajectories = mutableListOf<CompositeTrajectory2D>()
for (i in listOf(Trajectory2D.L, Trajectory2D.R)) {
for (j in listOf(Trajectory2D.L, Trajectory2D.R)) {
val finalCircle = finalCircles[j]!!
val finalObstacle = Obstacle(listOf(finalCircle))
//Using obstacle to minimize code bloat
val finalObstacle = Obstacle(finalCircles[j])
var currentPaths: List<TangentPath> = listOf(
TangentPath(
//We need only the direction of the final segment from this
Tangent(
initialCircles[i]!!,
initialCircles[i]!!,
Obstacle(listOf(initialCircles[i]!!)),
Obstacle(listOf(initialCircles[i]!!)),
initialCircles[i],
initialCircles[i],
Obstacle(initialCircles[i]),
Obstacle(initialCircles[i]),
LineSegment(start, start),
i
)
)
)
while (!allFinished(currentPaths, finalObstacle)) {
// paths after next obstacle iteration
val newPaths = mutableListOf<TangentPath>()
// for each path propagate it one obstacle further
for (tangentPath: TangentPath in currentPaths) {
val currentCircle = tangentPath.last().endCircle
val currentDirection: Trajectory2D.Direction = tangentPath.last().endDirection
val currentObstacle = tangentPath.last().endObstacle
var nextObstacle: Obstacle? = null
if (currentObstacle != finalObstacle) {
val tangentToFinal: Tangent? = outerTangents(currentObstacle, finalObstacle)[DubinsPath.Type(
// If path is finished, ignore it
// TODO avoid returning to ignored obstacle on the next cycle
if (currentObstacle == finalObstacle) {
newPaths.add(tangentPath)
} else {
val tangentToFinal: Tangent = outerTangents(currentObstacle, finalObstacle)[DubinsPath.Type(
currentDirection,
Trajectory2D.S,
j
)]
for (obstacle in sortedObstacles(currentObstacle, obstacles)) {
if (tangentToFinal!!.intersectObstacle(obstacle)) {
nextObstacle = obstacle
break
}
}
if (nextObstacle == null) {
nextObstacle = finalObstacle
}
val nextTangents: Map<DubinsPath.Type, Tangent> = outerTangents(currentObstacle, nextObstacle)
.filter { (key, tangent) ->
obstacles.none { obstacle -> tangent.intersectObstacle(obstacle) } &&
key.first == currentDirection &&
(nextObstacle != finalObstacle || key.third == j)
}
)] ?: TODO("Intersecting obstacles are not supported")
var tangentsAlong: List<Tangent>
for (tangent in nextTangents.values) {
if (tangent.startCircle == tangentPath.last().endCircle) {
val lengthMaxPossible = arcLength(
tangent.startCircle,
tangentPath.last().lineSegment.end,
tangent.startObstacle.nextTangent(
tangent.startCircle,
currentDirection
).lineSegment.begin,
currentDirection
)
val lengthCalculated = arcLength(
tangent.startCircle,
tangentPath.last().lineSegment.end,
tangent.lineSegment.begin,
currentDirection
)
tangentsAlong = if (lengthCalculated > lengthMaxPossible) {
tangentsAlongTheObstacle(
currentCircle,
currentDirection,
tangent.startCircle,
currentObstacle
)
} else {
// searching for the nearest obstacle that intersects with the direct path
val nextObstacle = sortedObstacles(currentObstacle, obstacles).find { obstacle ->
tangentToFinal.intersectsObstacle(obstacle)
} ?: finalObstacle
//TODO add break check for end of path
// All valid tangents from current obstacle to the next one
val nextTangents: Collection<Tangent> = outerTangents(
currentObstacle,
nextObstacle
).filter { (key, tangent) ->
obstacles.none { obstacle -> tangent.intersectsObstacle(obstacle) } && // does not intersect other obstacles
key.first == currentDirection && // initial direction is the same as end of previous segment direction
(nextObstacle != finalObstacle || key.third == j) // if it is the last, it should be the same as the one we are searching for
}.values
for (tangent in nextTangents) {
val tangentsAlong = if (tangent.startCircle == tangentPath.last().endCircle) {
//if the previous segment last circle is the same as first circle of the next segment
if (tangent.startObstacle.circles.size < 2){
emptyList()
} else {
val lengthMaxPossible = arcLength(
tangent.startCircle,
tangentPath.last().lineSegment.end,
tangent.startObstacle.nextTangent(
tangent.startCircle,
currentDirection
).lineSegment.begin,
currentDirection
)
val lengthCalculated = arcLength(
tangent.startCircle,
tangentPath.last().lineSegment.end,
tangent.lineSegment.begin,
currentDirection
)
if (lengthCalculated > lengthMaxPossible) {
tangentsAlongTheObstacle(
currentCircle,
currentDirection,
tangent.startCircle,
currentObstacle
)
} else {
emptyList()
}
}
} else {
tangentsAlong = tangentsAlongTheObstacle(
tangentsAlongTheObstacle(
currentCircle,
currentDirection,
tangent.startCircle,
@ -575,8 +540,6 @@ internal fun findAllPaths(
}
newPaths.add(TangentPath(tangentPath.tangents + tangentsAlong + tangent))
}
} else {
newPaths.add(tangentPath)
}
}
currentPaths = newPaths
@ -584,7 +547,7 @@ internal fun findAllPaths(
trajectories += currentPaths.map { tangentPath ->
val lastDirection: Trajectory2D.Direction = tangentPath.last().endDirection
val end = finalCircles[j]!!
val end = finalCircles[j]
TangentPath(
tangentPath.tangents +
Tangent(

6
trajectory-kt/src/commonTest/kotlin/space/kscience/kmath/trajectory/ObstacleTest.kt
View File

@ -21,11 +21,7 @@ class ObstacleTest {
val finalRadius = 0.5
val obstacles = listOf(
Obstacle(
listOf(
Circle2D(vector(7.0, 1.0), 5.0)
)
)
Obstacle(Circle2D(vector(7.0, 1.0), 5.0))
)
val outputTangents = findAllPaths(

4
trajectory-kt/src/commonTest/kotlin/space/kscience/kmath/trajectory/TangentTest.kt
View File

@ -44,7 +44,7 @@ class TangentTest {
)
)
val tangentMap = tangentsToCircle(c1, c2)
val tangentMap = tangentsBetweenCircles(c1, c2)
val tangentMapKeys = tangentMap.keys.toList()
val tangentMapValues = tangentMap.values.toList()
@ -58,6 +58,6 @@ class TangentTest {
fun concentric(){
val c1 = Circle2D(vector(0.0, 0.0), 10.0)
val c2 = Circle2D(vector(0.0, 0.0), 1.0)
assertEquals(emptyMap(), tangentsToCircle(c1, c2))
assertEquals(emptyMap(), tangentsBetweenCircles(c1, c2))
}
}