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capsule.go
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capsule.go
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package spatialmath
import (
"encoding/json"
"fmt"
"math"
"sync"
"github.com/golang/geo/r3"
commonpb "go.viam.com/api/common/v1"
"go.viam.com/rdk/utils"
)
// capsule is a collision geometry that represents a capsule, it has a pose and a radius that fully define it.
//
// ....___________________
// .../ \
// .x| |-------O-------| |x
// ...\___________________/
//
// Length is the distance between the x's, or internal segment length + 2*radius.
type capsule struct {
// this is the pose of one end of the capsule. The full capsule extends `length` mm outwards in the direction of
// the pose's orientation
pose Pose
radius float64
length float64 // total length of the capsule, tip to tip
label string
// These values are generated at geometry creation time and should not be altered by hand
// They are stoed here because they are useful and expensive to calculate
segA r3.Vector // Proximal endpoint of capsule line segment. First point from `pose` to be surrounded by `radius` of capsule
segB r3.Vector // Distal endpoint of capsule line segment. Most distal point to be surrounded by `radius` of capsule
center r3.Vector // Centerpoint of capsule as an r3.Vector, cached to prevent recalculation
capVec r3.Vector // Vector pointing from `center` towards `segB`, cached to prevent recalculation
rotMatrix *RotationMatrix
once sync.Once
}
// NewCapsule instantiates a new capsule Geometry.
func NewCapsule(offset Pose, radius, length float64, label string) (Geometry, error) {
if radius <= 0 || length <= 0 {
return nil, newBadGeometryDimensionsError(&capsule{})
}
if length < radius*2 {
return nil, newBadCapsuleLengthError(length, radius)
}
if length == radius*2 {
return NewSphere(offset, radius, label)
}
return newCapsuleWithSegPoints(offset, radius, length, label), nil
}
// Will precalculate the linear endpoints for a capsule.
func newCapsuleWithSegPoints(offset Pose, radius, length float64, label string) Geometry {
segA := Compose(offset, NewPoseFromPoint(r3.Vector{0, 0, -length/2 + radius})).Point()
segB := Compose(offset, NewPoseFromPoint(r3.Vector{0, 0, length/2 - radius})).Point()
center := offset.Point()
return &capsule{
pose: offset,
radius: radius,
length: length,
label: label,
segA: segA,
segB: segB,
center: center,
capVec: segB.Sub(center),
}
}
func (c *capsule) MarshalJSON() ([]byte, error) {
config, err := NewGeometryConfig(c)
if err != nil {
return nil, err
}
config.Type = "capsule"
config.R = c.radius
config.L = c.length
return json.Marshal(config)
}
// String returns a human readable string that represents the capsule.
func (c *capsule) String() string {
return fmt.Sprintf("Type: Capsule, Radius: %.0f, Length: %.0f", c.radius, c.length)
}
// Label returns the label of this capsule.
func (c *capsule) Label() string {
return c.label
}
// SetLabel sets the label of this capsule.
func (c *capsule) SetLabel(label string) {
c.label = label
}
// Pose returns the pose of the capsule.
func (c *capsule) Pose() Pose {
return c.pose
}
// AlmostEqual compares the capsule with another geometry and checks if they are equivalent.
func (c *capsule) AlmostEqual(g Geometry) bool {
other, ok := g.(*capsule)
if !ok {
return false
}
return PoseAlmostEqualEps(c.pose, other.pose, 1e-6) &&
utils.Float64AlmostEqual(c.radius, other.radius, 1e-8) &&
utils.Float64AlmostEqual(c.length, other.length, 1e-8)
}
// Transform premultiplies the capsule pose with a transform, allowing the capsule to be moved in space.
func (c *capsule) Transform(toPremultiply Pose) Geometry {
newPose := Compose(toPremultiply, c.pose)
segB := Compose(toPremultiply, NewPoseFromPoint(c.segB)).Point()
center := newPose.Point()
return &capsule{
pose: newPose,
radius: c.radius,
length: c.length,
label: c.label,
segA: Compose(toPremultiply, NewPoseFromPoint(c.segA)).Point(),
segB: segB,
center: center,
capVec: segB.Sub(center),
}
}
// ToProto converts the capsule to a Geometry proto message.
func (c *capsule) ToProtobuf() *commonpb.Geometry {
return &commonpb.Geometry{
Center: PoseToProtobuf(c.pose),
GeometryType: &commonpb.Geometry_Capsule{
Capsule: &commonpb.Capsule{
RadiusMm: c.radius,
LengthMm: c.length,
},
},
Label: c.label,
}
}
// CollidesWith checks if the given capsule collides with the given geometry and returns true if it does.
func (c *capsule) CollidesWith(g Geometry) (bool, error) {
if other, ok := g.(*box); ok {
return capsuleVsBoxCollision(c, other), nil
}
dist, err := c.DistanceFrom(g)
if err != nil {
return true, err
}
return dist <= CollisionBuffer, nil
}
// CollidesWith checks if the given capsule collides with the given geometry and returns true if it does.
func (c *capsule) DistanceFrom(g Geometry) (float64, error) {
if other, ok := g.(*box); ok {
return capsuleVsBoxDistance(c, other), nil
}
if other, ok := g.(*capsule); ok {
return capsuleVsCapsuleDistance(c, other), nil
}
if other, ok := g.(*point); ok {
return capsuleVsPointDistance(c, other.position), nil
}
if other, ok := g.(*sphere); ok {
return capsuleVsSphereDistance(c, other), nil
}
return math.Inf(-1), newCollisionTypeUnsupportedError(c, g)
}
func (c *capsule) EncompassedBy(g Geometry) (bool, error) {
if other, ok := g.(*capsule); ok {
return capsuleInCapsule(c, other), nil
}
if other, ok := g.(*box); ok {
return capsuleInBox(c, other), nil
}
if other, ok := g.(*sphere); ok {
return capsuleInSphere(c, other), nil
}
if _, ok := g.(*point); ok {
return false, nil
}
return true, newCollisionTypeUnsupportedError(c, g)
}
// ToPoints converts a capsule geometry into []r3.Vector. This method takes one argument which determines
// how many points should like on the capsule's surface. If the argument is set to 0. we automatically
// substitute the value with defaultTotalSpherePoints.
func (c *capsule) ToPoints(resolution float64) []r3.Vector {
if resolution <= 0 {
resolution = defaultPointDensity
}
s := &sphere{pose: NewZeroPose(), radius: c.radius}
vecList := s.ToPoints(resolution)
// move points to be correctly located on capsule endcaps
adj := c.length/2 - c.radius
for _, pt := range vecList {
if pt.Z >= 0 {
pt.Z += adj
} else {
pt.Z -= adj
}
}
// Now distribute points along the cylindrical shaft
totalShaftPts := (c.radius * c.length) * resolution
ptsPerRing := totalShaftPts / (c.length * resolution)
ringCnt := math.Floor(totalShaftPts / ptsPerRing)
zInc := c.length / (ringCnt + 1)
for ring := 1.; ring <= ringCnt; ring++ {
for ringPt := 0.; ringPt < ptsPerRing; ringPt++ {
theta := 2. * math.Pi * (ringPt / ptsPerRing)
vecList = append(vecList, r3.Vector{math.Cos(theta) * c.radius, math.Sin(theta) * c.radius, zInc * ring})
}
}
return transformPointsToPose(vecList, c.Pose())
}
// rotationMatrix returns the cached matrix if it exists, and generates it if not.
func (c *capsule) rotationMatrix() *RotationMatrix {
c.once.Do(func() { c.rotMatrix = c.pose.Orientation().RotationMatrix() })
return c.rotMatrix
}
func capsuleVsPointDistance(c *capsule, other r3.Vector) float64 {
return DistToLineSegment(c.segA, c.segB, other) - c.radius
}
func capsuleVsSphereDistance(c *capsule, other *sphere) float64 {
return DistToLineSegment(c.segA, c.segB, other.pose.Point()) - (c.radius + other.radius)
}
func capsuleVsCapsuleDistance(c, other *capsule) float64 {
return SegmentDistanceToSegment(c.segA, c.segB, other.segA, other.segB) - (c.radius + other.radius)
}
func capsuleVsBoxDistance(c *capsule, other *box) float64 {
// Large amounts of capsule collision code were adopted from `brax`
// https://github.com/google/brax/blob/7eaa16b4bf446b117b538dbe9c9401f97cf4afa2/brax/physics/colliders.py
// https://github.com/google/brax/blob/7eaa16b4bf446b117b538dbe9c9401f97cf4afa2/brax/physics/geometry.py
// Brax converts boxes to meshes composed of 12 triangles and does collision detection on those.
// SAT is faster and easier if we are *NOT* GPU-accelerated. But triangle method is guaranteed accurate at distances.
dist := capsuleBoxSeparatingAxisDistance(c, other)
// Separating axis theorum provides accurate penetration depth but is not accurate for separation
// if we are not in collision, convert box to mesh and determine triangle-capsule separation distance
if dist > CollisionBuffer {
return capsuleVsMeshDistance(c, other.toMesh())
}
return dist
}
// IMPORTANT: meshes are not considered solid. A mesh is not guaranteed to represent an enclosed area. This will measure ONLY the distance
// to the closest triangle in the mesh.
func capsuleVsMeshDistance(c *capsule, other *mesh) float64 {
lowDist := math.Inf(1)
for _, t := range other.triangles {
// Measure distance to each mesh triangle
dist := capsuleVsTriangleDistance(c, t)
if dist < lowDist {
lowDist = dist
}
}
return lowDist
}
func capsuleVsTriangleDistance(c *capsule, other *triangle) float64 {
capPt, triPt := closestPointsSegmentTriangle(c.segA, c.segB, other)
return capPt.Sub(triPt).Norm() - c.radius
}
// capsuleInCapsule returns a bool describing if the inner capsule is fully encompassed by the outer capsule.
func capsuleInCapsule(inner, outer *capsule) bool {
return capsuleVsPointDistance(outer, inner.segA) < -inner.radius &&
capsuleVsPointDistance(outer, inner.segB) < -inner.radius
}
// capsuleInBox returns a bool describing if the given capsule is fully encompassed by the given box.
func capsuleInBox(c *capsule, b *box) bool {
return pointVsBoxDistance(c.segA, b) <= -c.radius && pointVsBoxDistance(c.segB, b) <= -c.radius
}
// capsuleInSphere returns a bool describing if the given capsule is fully encompassed by the given sphere.
func capsuleInSphere(c *capsule, s *sphere) bool {
return c.segA.Sub(s.pose.Point()).Norm()+c.radius <= s.radius && c.segB.Sub(s.pose.Point()).Norm()+c.radius <= s.radius
}
// capsuleVsBoxCollision returns immediately as soon as any result is found indicating that the two objects are not in collision.
func capsuleVsBoxCollision(c *capsule, b *box) bool {
centerDist := b.pose.Point().Sub(c.center)
// check if there is a distance between bounding spheres to potentially exit early
if centerDist.Norm()-((c.length/2)+b.boundingSphereR) > CollisionBuffer {
return false
}
rmA := c.rotationMatrix()
rmB := b.rotationMatrix()
// Capsule is modeled as a 0x0xN box, where N = (length/2)-radius.
// This allows us to check separating axes on a reduced set of projections.
cutoff := CollisionBuffer + c.radius
for i := 0; i < 3; i++ {
if separatingAxisTest1D(¢erDist, &c.capVec, rmA.Row(i), b.halfSize, rmB) > cutoff {
return false
}
if separatingAxisTest1D(¢erDist, &c.capVec, rmB.Row(i), b.halfSize, rmB) > cutoff {
return false
}
for j := 0; j < 3; j++ {
crossProductPlane := rmA.Row(i).Cross(rmB.Row(j))
// if edges are parallel, this check is already accounted for by one of the face projections, so skip this case
if !utils.Float64AlmostEqual(crossProductPlane.Norm(), 0, floatEpsilon) {
if separatingAxisTest1D(¢erDist, &c.capVec, crossProductPlane, b.halfSize, rmB) > cutoff {
return false
}
}
}
}
return true
}
func capsuleBoxSeparatingAxisDistance(c *capsule, b *box) float64 {
centerDist := b.pose.Point().Sub(c.center)
// check if there is a distance between bounding spheres to potentially exit early
if boundingSphereDist := centerDist.Norm() - ((c.length / 2) + b.boundingSphereR); boundingSphereDist > CollisionBuffer {
return boundingSphereDist
}
rmA := c.rotationMatrix()
rmB := b.rotationMatrix()
// Capsule is modeled as a 0x0xN box, where N = (length/2)-radius.
// This allows us to check separating axes on a reduced set of projections.
max := math.Inf(-1)
for i := 0; i < 3; i++ {
if separation := separatingAxisTest1D(¢erDist, &c.capVec, rmA.Row(i), b.halfSize, rmB); separation > max {
max = separation
}
if separation := separatingAxisTest1D(¢erDist, &c.capVec, rmB.Row(i), b.halfSize, rmB); separation > max {
max = separation
}
for j := 0; j < 3; j++ {
crossProductPlane := rmA.Row(i).Cross(rmB.Row(j))
// if edges are parallel, this check is already accounted for by one of the face projections, so skip this case
if !utils.Float64AlmostEqual(crossProductPlane.Norm(), 0, floatEpsilon) {
if separation := separatingAxisTest1D(¢erDist, &c.capVec, crossProductPlane, b.halfSize, rmB); separation > max {
max = separation
}
}
}
}
return max - c.radius
}
func separatingAxisTest1D(positionDelta, capVec *r3.Vector, plane r3.Vector, halfSizeB [3]float64, rmB *RotationMatrix) float64 {
sum := math.Abs(positionDelta.Dot(plane))
for i := 0; i < 3; i++ {
sum -= math.Abs(rmB.Row(i).Mul(halfSizeB[i]).Dot(plane))
}
sum -= math.Abs(capVec.Dot(plane))
return sum
}