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Simbody
3.5
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Simbody
3.5
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A 3d rectangular box aligned with an unspecified frame F and centered at that frame's origin. More...
Public Member Functions | |
| Box_ () | |
| Construct an uninitialized Box object; the dimensions will be garbage. More... | |
| Box_ (const Vec3P &halfLengths) | |
| Construct a Box with the given nonnegative half-dimensions. More... | |
| Box_ & | setHalfLengths (const Vec3P &halfLengths) |
| Change the half-dimensions of this box. More... | |
| Box_ & | addToHalfLengths (const Vec3P &incr) |
| Change the half-dimensions of this box by adding the given vector. More... | |
| const Vec3P & | getHalfLengths () const |
| Return the half-lengths of this box as a Vec3 from the center to the first quadrant vertex. More... | |
| RealP | getOrderedHalfLength (int i) const |
| Get lengths in order shortest to longest; 0 is shortest, 2 is longest. More... | |
| CoordinateAxis | getOrderedAxis (int i) const |
| Get axes in order shortest to longest; 0 is shortest, 2 is longest. More... | |
| RealP | findVolume () const |
| Calculate the volume of this box. More... | |
| RealP | findArea () const |
| Calculate the surface area of this box, ignoring degeneracy (meaning that all pairs of sides are counted even if coincident). More... | |
| bool | containsPoint (const Vec3P &pt) const |
| Given a point measured and expressed in the box frame, determine whether it is inside the box (we count touching the surface as inside). More... | |
| Vec3P | findClosestPointOfSolidBox (const Vec3P &pt, bool &ptWasInside) const |
| Given a point location in the box frame, return the closest point of the solid box, and a flag saying whether the given point was inside the box, using the same definition of "inside" as the containsPoint() method. More... | |
| Vec3P | findClosestPointOnSurface (const Vec3P &pt, bool &ptWasInside) const |
| Given a point location in the box frame, return the closest point on the box surface, and a flag saying whether the given point was inside the box, using the same definition of "inside" as the containsPoint() method. More... | |
| RealP | findDistanceSqrToPoint (const Vec3P &pt) const |
| Return the square of the distance from this box to a given point whose location is measured from and expressed in the box frame (at the box center). More... | |
| Vec3P | findSupportPoint (const Vec3 &d) const |
| Find a supporting point on the surface of the box in the given direction, which must be expressed in the box frame. More... | |
| RealP | findDistanceSqrToSphere (const Geo::Sphere_< P > &sphere) const |
| Return the square of the distance from this box to a given sphere whose center location is measured from and expressed in the box frame (at the box center). More... | |
| RealP | findDistanceSqrToAlignedBox (const Geo::AlignedBox_< P > &aab) const |
| Return the square of the distance from this box to an axis-aligned box whose center location is measured from and expressed in this box frame (at the box center). More... | |
| bool | intersectsSphere (const Geo::Sphere_< P > &sphere) const |
| Given a sphere with center measured and expressed in the box frame, return true if the box and sphere intersect. More... | |
| bool | intersectsAlignedBox (const Geo::AlignedBox_< P > &aab) const |
| Given an aligned box with center measured and expressed in the from of this box, return true if the two boxes intersect. More... | |
| bool | intersectsOrientedBox (const Geo::OrientedBox_< P > &ob) const |
| Given an oriented box whose pose is measured and expressed in the frame of this box, return true if the two boxes intersect. More... | |
| bool | mayIntersectOrientedBox (const Geo::OrientedBox_< P > &ob) const |
| Given an oriented box whose pose is measured and expressed in the frame of this box, return true if the two boxes may be intersecting. More... | |
Box mesh methods | |
Methods to use if you want to think of the box as a convex mesh. | |
| Vec3P | getVertexPos (int vx) const |
| Use bits in the vertex number to pick the signs, with 0=negative, 1=positive: More... | |
| int | findSupportVertex (const Vec3P &d) const |
| Find the vertex (0-7) that is furthest in the direction d, which is given in the box frame. More... | |
| UnitVec3P | getVertexNormal (int vx) const |
| Vertex normals point diagonally outwards from the box corners. More... | |
| Vec3P | getEdgeCenter (int ex) const |
| Return the center point of the specified edge, in the box frame. More... | |
| UnitVec3P | getEdgeNormal (int ex) const |
| Edge normals point diagonally outwards from the edge. More... | |
| CoordinateDirection | getEdgeCoordinateDirection (int ex) const |
| Return the direction of an edge, going from its first vertex to its second vertex, as a CoordinateDirection. More... | |
| UnitVec3P | getEdgeDirection (int ex) const |
| Return a unit vector aligned with the selected edge, pointing in the direction from the first vertex towards the second vertex, in the box frame. More... | |
| CoordinateDirection | getFaceCoordinateDirection (int fx) const |
| Return the outward normal for the given face as a CoordinateDirection. More... | |
| Vec3P | getFaceCenter (int fx) const |
| Return the center point position for the given face. More... | |
| UnitVec3P | getFaceNormal (int fx) const |
| Return the outward normal for the given face as a unit vector in the box frame. More... | |
| void | getFaceVertices (int fx, int v[4]) const |
| A face has four vertices ordered counterclockwise about the face normal. More... | |
| void | getVertexFaces (int vx, int f[3], int w[3]) const |
| Each vertex has three incident faces. More... | |
| void | getEdgeVertices (int ex, int v[2]) const |
| An edge connects two vertices. More... | |
| void | getVertexEdges (int vx, int e[3], int w[3]) const |
| Each vertex has three incident edges. More... | |
| void | getFaceEdges (int fx, int e[4]) const |
| A face has four edges, ordered by the vertex ordering: v0-v1, v1-v2, v2-v3, v3-v1. More... | |
| void | getEdgeFaces (int ex, int f[2], int w[2]) const |
| An edge is between two faces. More... | |
| static int | getNumVertices () |
| Use bits in the vertex number to pick the signs, with 0=negative, 1=positive: More... | |
| static int | getNumEdges () |
| Use bits in the vertex number to pick the signs, with 0=negative, 1=positive: More... | |
| static int | getNumFaces () |
| Use bits in the vertex number to pick the signs, with 0=negative, 1=positive: More... | |
A 3d rectangular box aligned with an unspecified frame F and centered at that frame's origin.
The box has a local frame B, centered at the box center and oriented along the box edges, and B==F. We keep track of the relative edge lengths to facilitate short-to-long processing.
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Construct an uninitialized Box object; the dimensions will be garbage.
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Construct a Box with the given nonnegative half-dimensions.
Cost is 4 flops to sort the edges.
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Change the half-dimensions of this box.
Dimensions must be nonnegative. Cost is 4 flops to sort the edges.
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Change the half-dimensions of this box by adding the given vector.
The result must be nonnegative. Cost is 7 flops, including resorting the edges.
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Return the half-lengths of this box as a Vec3 from the center to the first quadrant vertex.
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Get lengths in order shortest to longest; 0 is shortest, 2 is longest.
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Get axes in order shortest to longest; 0 is shortest, 2 is longest.
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Calculate the volume of this box.
Cost is 4 flops.
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Calculate the surface area of this box, ignoring degeneracy (meaning that all pairs of sides are counted even if coincident).
Cost is 6 flops.
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Given a point measured and expressed in the box frame, determine whether it is inside the box (we count touching the surface as inside).
The point must be measured from the box center. Cost is about 5 flops.
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Given a point location in the box frame, return the closest point of the solid box, and a flag saying whether the given point was inside the box, using the same definition of "inside" as the containsPoint() method.
Here we define the closest point to an inside point to be the point itself. Cost is about 9 flops.
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Given a point location in the box frame, return the closest point on the box surface, and a flag saying whether the given point was inside the box, using the same definition of "inside" as the containsPoint() method.
Cost is about 9 flops for outside points, 18 for inside points.
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Return the square of the distance from this box to a given point whose location is measured from and expressed in the box frame (at the box center).
If the point is on or inside the box the returned distance is zero. Cost is about 14 flops.
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Find a supporting point on the surface of the box in the given direction, which must be expressed in the box frame.
The direction vector does not have to be a unit vector. The returned point will always be one of the eight vertices; we treat zeroes here as positive. Consequently if the input vector is exactly zero, the vertex in the positive orthant is returned as it would be if the input direction were (1,1,1). Cost is about 5 flops.
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Return the square of the distance from this box to a given sphere whose center location is measured from and expressed in the box frame (at the box center).
If the sphere intersects the box the returned distance is zero. Cost is about 17 flops.
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Return the square of the distance from this box to an axis-aligned box whose center location is measured from and expressed in this box frame (at the box center).
If the boxes intersect the returned distance is zero. Cost is about 17 flops.
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Given a sphere with center measured and expressed in the box frame, return true if the box and sphere intersect.
We are treating both objects as solids, so we'll say yes even if one object completely contains the other. We also return true if they are just touching. Cost is about 8 flops.
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Given an aligned box with center measured and expressed in the from of this box, return true if the two boxes intersect.
We are treating both objects as solids, so we'll say yes even if one box completely contains the other. We also return true if they are just touching. Cost is about 8 flops.
| bool SimTK::Geo::Box_< P >::intersectsOrientedBox | ( | const Geo::OrientedBox_< P > & | ob | ) | const |
Given an oriented box whose pose is measured and expressed in the frame of this box, return true if the two boxes intersect.
We are treating both objects as solids, so we'll say yes even if one box completely contains the other. We also return true if they are just touching. This is an exact but fairly expensive test if the boxes are separated; if you don't mind some false positives, use mayIntersectOrientedBox() instead. Cost is about 200 flops worst case (when boxes are intersecting) although it can return false in as few as 16 flops.
| bool SimTK::Geo::Box_< P >::mayIntersectOrientedBox | ( | const Geo::OrientedBox_< P > & | ob | ) | const |
Given an oriented box whose pose is measured and expressed in the frame of this box, return true if the two boxes may be intersecting.
Only relatively cheap operations are performed at the expense of returning false positives sometimes (allegedly less than 10% of the time). If you need an exact determination, use intersectsOrientedBox(). Cost is about 75 flops worst case (when boxes appear to be intersecting) but can return false in as few as 16 flops.
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inlinestatic |
Use bits in the vertex number to pick the signs, with 0=negative, 1=positive:
000 -hx -hy -hz
001 -hx -hy hz
...
111 hx hy hz
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inlinestatic |
Use bits in the vertex number to pick the signs, with 0=negative, 1=positive:
000 -hx -hy -hz
001 -hx -hy hz
...
111 hx hy hz
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inlinestatic |
Use bits in the vertex number to pick the signs, with 0=negative, 1=positive:
000 -hx -hy -hz
001 -hx -hy hz
...
111 hx hy hz
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inline |
Use bits in the vertex number to pick the signs, with 0=negative, 1=positive:
000 -hx -hy -hz
001 -hx -hy hz
...
111 hx hy hz
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Find the vertex (0-7) that is furthest in the direction d, which is given in the box frame.
Zero coordinates in d are treated as though positive.
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Vertex normals point diagonally outwards from the box corners.
These are unit vectors with each coordinate +/- 1/sqrt(3).
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Return the center point of the specified edge, in the box frame.
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Edge normals point diagonally outwards from the edge.
These are unit vectors with one coordinate zero and the others +/- 1/sqrt(2).
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Return the direction of an edge, going from its first vertex to its second vertex, as a CoordinateDirection.
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Return a unit vector aligned with the selected edge, pointing in the direction from the first vertex towards the second vertex, in the box frame.
For a box, all edges are aligned with the coordinate system axes so the returned vector will have only one non-zero component which will be 1 or -1.
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Return the outward normal for the given face as a CoordinateDirection.
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Return the center point position for the given face.
This will be a vector with one non-zero component of magnitude equal to one of the box half-dimensions, with the appropriate sign.
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Return the outward normal for the given face as a unit vector in the box frame.
This will have only one non-zero component which will be 1 or -1.
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A face has four vertices ordered counterclockwise about the face normal.
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Each vertex has three incident faces.
Return the face numbers (0-5) and which of the four face vertices is this one (0-3).
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An edge connects two vertices.
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Each vertex has three incident edges.
Return the edge numbers (0-11) and which of the two edge vertices is this one (0-1).
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A face has four edges, ordered by the vertex ordering: v0-v1, v1-v2, v2-v3, v3-v1.
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An edge is between two faces.
Return the face numbers (0-5) and which one of the four edges on each face is this edge (0-3).
1.8.8