Class CPolyhedron
Defined in File CPolyhedron.h
Nested Relationships
Nested Types
Inheritance Relationships
Base Types
public mrpt::viz::CVisualObject(Class CVisualObject)public mrpt::viz::VisualObjectParams_Triangles(Class VisualObjectParams_Triangles)public mrpt::viz::VisualObjectParams_Lines(Class VisualObjectParams_Lines)
Class Documentation
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class CPolyhedron : public virtual mrpt::viz::CVisualObject, public mrpt::viz::VisualObjectParams_Triangles, public mrpt::viz::VisualObjectParams_Lines
This class represents arbitrary polyhedra. The class includes a set of static methods to create common polyhedrons. The class includes many methods to create standard polyhedra, not intended to be fast but to be simple. For example, the dodecahedron is not created efficiently: first, an icosahedron is created, and a duality operator is applied to it, which yields the dodecahedron. This way, code is much smaller, although much slower. This is not a big problem, since polyhedron creation does not usually take a significant amount of time (they are created once and rendered many times). Polyhedra information and models have been gotten from the Wikipedia, https://wikipedia.org
See also
opengl::Scene
Polyhedron special operations.
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CPolyhedron::Ptr getDual() const
Given a polyhedron, creates its dual.
See also
- Throws:
std::logic_error – Can’t get the dual to this polyhedron.
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CPolyhedron::Ptr truncate(double factor) const
Truncates a polyhedron to a given factor.
See also
- Throws:
std::logic_error – Polyhedron truncation results in skew polygons and thus it’s impossible to perform.
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CPolyhedron::Ptr cantellate(double factor) const
Cantellates a polyhedron to a given factor.
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CPolyhedron::Ptr augment(double height) const
Augments a polyhedron to a given height. This operation is roughly dual to the truncation: given a body P, the operation dtdP and aP yield resembling results.
See also
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CPolyhedron::Ptr augment(double height, size_t numVertices) const
Augments a polyhedron to a given height. This method only affects to faces with certain number of vertices.
See also
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CPolyhedron::Ptr augment(bool direction = false) const
Augments a polyhedron, so that the resulting triangles are equilateral. If the argument is true, triangles are “cut” from the polyhedron, instead of being added.
See also
- Throws:
std::logic_error – a non-regular face has been found.
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CPolyhedron::Ptr augment(size_t numVertices, bool direction = false) const
Augments a polyhedron, so that the resulting triangles are equilateral; affects only faces with certain number of faces. If the second argument is true, triangles are “cut” from the polyhedron.
See also
- Throws:
std::logic_error – a non-regular face has been found.
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CPolyhedron::Ptr rotate(double angle) const
Rotates a polyhedron around the Z axis a given amount of radians. In some cases, this operation may be necessary to view the symmetry between related objects.
See also
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CPolyhedron::Ptr scale(double factor) const
Scales a polyhedron to a given factor.
See also
- Throws:
std::logic_error – factor is not a strictly positive number.
Platonic solids.
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static CPolyhedron::Ptr CreateTetrahedron(double radius)
Creates a regular tetrahedron (see http://en.wikipedia.org/wiki/Tetrahedron). The tetrahedron is created as a triangular pyramid whose edges and vertices are transitive. The tetrahedron is the dual to itself.
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static CPolyhedron::Ptr CreateHexahedron(double radius)
Creates a regular cube, also called hexahedron (see http://en.wikipedia.org/wiki/Hexahedron). The hexahedron is created as a cubic prism which transitive edges. Another ways to create it include:
Dual to an octahedron.
Parallelepiped with three orthogonal, equally-lengthed vectors.
Triangular trapezohedron with proper height.
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static CPolyhedron::Ptr CreateOctahedron(double radius)
Creates a regular octahedron (see http://en.wikipedia.org/wiki/Octahedron). The octahedron is created as a square bipyramid whit transitive edges and vertices. Another ways to create an octahedron are:
Dual to an hexahedron
Triangular antiprism with transitive vertices.
Conveniently truncated tetrahedron.
See also
CreateHexahedron,getDual,CreateArchimedeanAntiprism,CreateTetrahedron,truncate,CreateTruncatedOctahedron,CreateTruncatedHexahedron,CreateCuboctahedron,CreateRhombicuboctahedron
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static CPolyhedron::Ptr CreateDodecahedron(double radius)
Creates a regular dodecahedron (see http://en.wikipedia.org/wiki/Dodecahedron). The dodecahedron is created as the dual to an icosahedron.
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static CPolyhedron::Ptr CreateIcosahedron(double radius)
Creates a regular icosahedron (see http://en.wikipedia.org/wiki/Icosahedron). The icosahedron is created as a gyroelongated pentagonal bipyramid with transitive edges, and it’s the dual to a dodecahedron.
Archimedean solids.
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static CPolyhedron::Ptr CreateTruncatedTetrahedron(double radius)
Creates a truncated tetrahedron, consisting of four triangular faces and for hexagonal ones (see http://en.wikipedia.org/wiki/Truncated_tetrahedron). Its dual is the triakis tetrahedron.
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static CPolyhedron::Ptr CreateCuboctahedron(double radius)
Creates a cuboctahedron, consisting of six square faces and eight triangular ones (see http://en.wikipedia.org/wiki/Cuboctahedron). There are several ways to create a cuboctahedron:
Hexahedron truncated to a certain extent.
Octahedron truncated to a certain extent.
Cantellated tetrahedron
Dual to a rhombic dodecahedron.
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static CPolyhedron::Ptr CreateTruncatedHexahedron(double radius)
Creates a truncated hexahedron, with six octogonal faces and eight triangular ones (see http://en.wikipedia.org/wiki/Truncated_hexahedron). The truncated octahedron is dual to the triakis octahedron.
See also
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static CPolyhedron::Ptr CreateTruncatedOctahedron(double radius)
Creates a truncated octahedron, with eight hexagons and eight squares (see http://en.wikipedia.org/wiki/Truncated_octahedron). It’s the dual to the tetrakis hexahedron.
See also
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static CPolyhedron::Ptr CreateRhombicuboctahedron(double radius, bool type = true)
Creates a rhombicuboctahedron, with 18 squares and 8 triangles (see http://en.wikipedia.org/wiki/Rhombicuboctahedron), calculated as an elongated square bicupola. It can also be calculated as a cantellated hexahedron or octahedron, and its dual is the deltoidal icositetrahedron. If the second argument is set to false, the lower cupola is rotated, so that the objet created is an elongated square gyrobicupola (see http://en.wikipedia.org/wiki/Elongated_square_gyrobicupola). This is not an archimedean solid, but a Johnson one, since it hasn’t got vertex transitivity.
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static CPolyhedron::Ptr CreateIcosidodecahedron(double radius, bool type = true)
Creates an icosidodecahedron, with 12 pentagons and 20 triangles (see http://en.wikipedia.org/wiki/Icosidodecahedron). Certain truncations of either a dodecahedron or an icosahedron yield an icosidodecahedron. The dual of the icosidodecahedron is the rhombic triacontahedron. If the second argument is set to false, the lower rotunda is rotated. In this case, the object created is a pentagonal orthobirotunda (see http://en.wikipedia.org/wiki/Pentagonal_orthobirotunda). This object presents symmetry against the XY plane and is not vertex transitive, so it’s a Johnson’s solid.
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static CPolyhedron::Ptr CreateTruncatedDodecahedron(double radius)
Creates a truncated dodecahedron, consisting of 12 dodecagons and 20 triangles (see http://en.wikipedia.org/wiki/Truncated_dodecahedron). The truncated dodecahedron is the dual to the triakis icosahedron.
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static CPolyhedron::Ptr CreateTruncatedIcosahedron(double radius)
Creates a truncated icosahedron, consisting of 20 hexagons and 12 pentagons. This object resembles a typical soccer ball (see http://en.wikipedia.org/wiki/Truncated_icosahedron). The pentakis dodecahedron is the dual to the truncated icosahedron.
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static CPolyhedron::Ptr CreateRhombicosidodecahedron(double radius)
Creates a rhombicosidodecahedron, consisting of 30 squares, 12 pentagons and 20 triangles (see http://en.wikipedia.org/wiki/Rhombicosidodecahedron). This object can be obtained as the cantellation of either a dodecahedron or an icosahedron. The dual of the rhombicosidodecahedron is the deltoidal hexecontahedron.
Other Johnson solids.
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static CPolyhedron::Ptr CreatePentagonalRotunda(double radius)
Creates a pentagonal rotunda (half an icosidodecahedron), consisting of six pentagons, ten triangles and a decagon (see http://en.wikipedia.org/wiki/Pentagonal_rotunda).
Catalan solids.
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static CPolyhedron::Ptr CreateTriakisTetrahedron(double radius)
Creates a triakis tetrahedron, dual to the truncated tetrahedron. This body consists of 12 isosceles triangles (see http://en.wikipedia.org/wiki/Triakis_tetrahedron).
See also
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static CPolyhedron::Ptr CreateRhombicDodecahedron(double radius)
Creates a rhombic dodecahedron, dual to the cuboctahedron. This body consists of 12 rhombi (see http://en.wikipedia.org/wiki/Rhombic_dodecahedron).
See also
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static CPolyhedron::Ptr CreateTriakisOctahedron(double radius)
Creates a triakis octahedron, dual to the truncated hexahedron. This body consists of 24 isosceles triangles (see http://en.wikipedia.org/wiki/Triakis_octahedron).
See also
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static CPolyhedron::Ptr CreateTetrakisHexahedron(double radius)
Creates a tetrakis hexahedron, dual to the truncated octahedron. This body consists of 24 isosceles triangles (see http://en.wikipedia.org/wiki/Tetrakis_hexahedron).
See also
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static CPolyhedron::Ptr CreateDeltoidalIcositetrahedron(double radius)
Creates a deltoidal icositetrahedron, dual to the rhombicuboctahedron. This body consists of 24 kites (see http://en.wikipedia.org/wiki/Deltoidal_icositetrahedron).
See also
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static CPolyhedron::Ptr CreateRhombicTriacontahedron(double radius)
Creates a rhombic triacontahedron, dual to the icosidodecahedron. This body consists of 30 rhombi (see http://en.wikipedia.org/wiki/Rhombic_triacontahedron).
See also
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static CPolyhedron::Ptr CreateTriakisIcosahedron(double radius)
Creates a triakis icosahedron, dual to the truncated dodecahedron. This body consists of 60 isosceles triangles http://en.wikipedia.org/wiki/Triakis_icosahedron).
See also
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static CPolyhedron::Ptr CreatePentakisDodecahedron(double radius)
Creates a pentakis dodecahedron, dual to the truncated icosahedron. This body consists of 60 isosceles triangles (see http://en.wikipedia.org/wiki/Pentakis_dodecahedron).
See also
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static CPolyhedron::Ptr CreateDeltoidalHexecontahedron(double radius)
Creates a deltoidal hexecontahedron, dual to the rhombicosidodecahedron. This body consists of 60 kites (see http://en.wikipedia.org/wiki/Deltoidal_hexecontahedron).
See also
Customizable polyhedra
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static CPolyhedron::Ptr CreateCubicPrism(double x1, double x2, double y1, double y2, double z1, double z2)
Creates a cubic prism, given the coordinates of two opposite vertices. Each edge will be parallel to one of the coordinate axes, although the orientation may change by assigning a pose to the object.
See also
CreateCubicPrism(const mrpt::math::TPoint3D &,const mrpt::math::TPoint3D &),CreateParallelepiped,CreateCustomPrism,CreateRegularPrism,CreateArchimedeanRegularPrism
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static CPolyhedron::Ptr CreateCubicPrism(const mrpt::math::TPoint3D &p1, const mrpt::math::TPoint3D &p2)
Creates a cubic prism, given two opposite vertices.
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static CPolyhedron::Ptr CreatePyramid(const std::vector<mrpt::math::TPoint2D> &baseVertices, double height)
Creates a custom pyramid, using a set of 2D vertices which will lie on the XY plane.
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static CPolyhedron::Ptr CreateDoublePyramid(const std::vector<mrpt::math::TPoint2D> &baseVertices, double height1, double height2)
Creates a double pyramid, using a set of 2D vertices which will lie on the XY plane. The second height is used with the downwards pointing pyramid, so that it will effectively point downwards if it’s positive.
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static CPolyhedron::Ptr CreateTruncatedPyramid(const std::vector<mrpt::math::TPoint2D> &baseVertices, double height, double ratio)
Creates a truncated pyramid, using a set of vertices which will lie on the XY plane. Do not try to use with a ratio equal to zero; use CreatePyramid instead. When using a ratio of 1, it will create a Prism.
See also
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static CPolyhedron::Ptr CreateFrustum(const std::vector<mrpt::math::TPoint2D> &baseVertices, double height, double ratio)
This is a synonym for CreateTruncatedPyramid.
See also
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static CPolyhedron::Ptr CreateCustomPrism(const std::vector<mrpt::math::TPoint2D> &baseVertices, double height)
Creates a custom prism with vertical edges, given any base which will lie on the XY plane.
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static CPolyhedron::Ptr CreateCustomAntiprism(const std::vector<mrpt::math::TPoint2D> &bottomBase, const std::vector<mrpt::math::TPoint2D> &topBase, double height)
Creates a custom antiprism, using two custom bases. For better results, the top base should be slightly rotated with respect to the bottom one.
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static CPolyhedron::Ptr CreateParallelepiped(const mrpt::math::TPoint3D &base, const mrpt::math::TPoint3D &v1, const mrpt::math::TPoint3D &v2, const mrpt::math::TPoint3D &v3)
Creates a parallelepiped, given a base point and three vectors represented as points.
See also
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static CPolyhedron::Ptr CreateBifrustum(const std::vector<mrpt::math::TPoint2D> &baseVertices, double height1, double ratio1, double height2, double ratio2)
Creates a bifrustum, or double truncated pyramid, given a base which will lie on the XY plane.
See also
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static CPolyhedron::Ptr CreateTrapezohedron(uint32_t numBaseEdges, double baseRadius, double basesDistance)
Creates a trapezohedron, consisting of 2*N kites, where N is the number of edges in the base. The base radius controls the polyhedron height, whilst the distance between bases affects the height. When the number of edges equals 3, the polyhedron is actually a parallelepiped, and it can even be a cube.
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static CPolyhedron::Ptr CreateRegularAntiprism(uint32_t numBaseEdges, double baseRadius, double height)
Creates an antiprism whose base is a regular polygon. The upper base is rotated \(\frac\pi N\) with respect to the lower one, where N is the number of vertices in the base, and thus the lateral triangles are isosceles.
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static CPolyhedron::Ptr CreateRegularPrism(uint32_t numBaseEdges, double baseRadius, double height)
Creates a regular prism whose base is a regular polygon and whose edges are either parallel or perpendicular to the XY plane.
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static CPolyhedron::Ptr CreateRegularPyramid(uint32_t numBaseEdges, double baseRadius, double height)
Creates a regular pyramid whose base is a regular polygon.
See also
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static CPolyhedron::Ptr CreateRegularDoublePyramid(uint32_t numBaseEdges, double baseRadius, double height1, double height2)
Creates a regular double pyramid whose base is a regular polygon.
See also
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static CPolyhedron::Ptr CreateArchimedeanRegularPrism(uint32_t numBaseEdges, double baseRadius)
Creates a regular prism whose lateral area is comprised of squares, and so each face of its is a regular polygon. Due to vertex transitivity, the resulting object is always archimedean.
See also
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static CPolyhedron::Ptr CreateArchimedeanRegularAntiprism(uint32_t numBaseEdges, double baseRadius)
Creates a regular antiprism whose lateral polygons are equilateral triangles, and so each face of its is a regular polygon. Due to vertex transitivity, the resulting object is always archimedean.
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static CPolyhedron::Ptr CreateRegularTruncatedPyramid(uint32_t numBaseEdges, double baseRadius, double height, double ratio)
Creates a regular truncated pyramid whose base is a regular polygon.
See also
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static CPolyhedron::Ptr CreateRegularFrustum(uint32_t numBaseEdges, double baseRadius, double height, double ratio)
This is a synonym for CreateRegularTruncatedPyramid.
See also
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static CPolyhedron::Ptr CreateRegularBifrustum(uint32_t numBaseEdges, double baseRadius, double height1, double ratio1, double height2, double ratio2)
Creates a bifrustum (double truncated pyramid) whose base is a regular polygon lying in the XY plane.
See also
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static CPolyhedron::Ptr CreateCupola(uint32_t numBaseEdges, double edgeLength)
Creates a cupola.
- Throws:
std::logic_error – if the number of edges is odd or less than four.
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static CPolyhedron::Ptr CreateCatalanTrapezohedron(uint32_t numBaseEdges, double height)
Creates a trapezohedron whose dual is exactly an archimedean antiprism. Creates a cube if numBaseEdges is equal to 3.
- Todo:
Actually resulting height is significantly higher than that passed to the algorithm.
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static CPolyhedron::Ptr CreateCatalanDoublePyramid(uint32_t numBaseEdges, double height)
Creates a double pyramid whose dual is exactly an archimedean prism. Creates an octahedron if numBaseEdges is equal to 4.
- Todo:
Actually resulting height is significantly higher than that passed to the algorithm.
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static CPolyhedron::Ptr CreateJohnsonSolidWithConstantBase(uint32_t numBaseEdges, double baseRadius, const std::string &components, size_t shifts = 0)
Creates a series of concatenated solids (most of which are prismatoids) whose base is a regular polygon with a given number of edges. Every face of the resulting body will be a regular polygon, so it is a Johnson solid; in special cases, it may be archimedean or even platonic. The shape of the body is defined by the string argument, which can include one or more of the following: Some examples of bodies are:
Public Functions
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virtual mrpt::math::TBoundingBoxf internalBoundingBoxLocal() const override
Evaluates the bounding box of this object (including possible children) in the coordinate frame of the object parent.
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virtual void updateBuffers() const override
Called by the rendering system to update internal geometry buffers.
Derived classes should override this to populate their data buffers (triangles, points, lines) when the object geometry changes.
This is called automatically when hasToUpdateBuffers() returns true, which happens after notifyChange() was called.
The base implementation does nothing; derived classes should override.
Note
Thread safety: implementations should lock the appropriate mutexes when writing to shared buffers.
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virtual bool traceRay(const mrpt::poses::CPose3D &o, double &dist) const override
Simulation of ray-trace, given a pose. Returns true if the ray effectively collisions with the object (returning the distance to the origin of the ray in “dist”), or false in other case. “dist” variable yields undefined behaviour when false is returned
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inline void getVertices(std::vector<mrpt::math::TPoint3D> &vertices) const
Gets a list with the polyhedron’s vertices.
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inline void getEdges(std::vector<TPolyhedronEdge> &edges) const
Gets a list with the polyhedron’s edges.
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inline void getFaces(std::vector<TPolyhedronFace> &faces) const
Gets a list with the polyhedron’s faces.
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inline uint32_t getNumberOfVertices() const
Gets the amount of vertices.
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inline uint32_t getNumberOfEdges() const
Gets the amount of edges.
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inline uint32_t getNumberOfFaces() const
Gets the amount of faces.
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void getEdgesLength(std::vector<double> &lengths) const
Gets a vector with each edge’s length.
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void getFacesArea(std::vector<double> &areas) const
Gets a vector with each face’s area. Won’t work properly if the polygons are not convex.
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double getVolume() const
Gets the polyhedron volume. Won’t work properly if the polyhedron is not convex.
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inline bool isWireframe() const
Returns whether the polyhedron will be rendered as a wireframe object.
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inline void setWireframe(bool enabled = true)
Sets whether the polyhedron will be rendered as a wireframe object.
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void getSetOfPolygons(std::vector<math::TPolygon3D> &vec) const
Gets the polyhedron as a set of polygons.
See also
mrpt::math::TPolygon3D
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void getSetOfPolygonsAbsolute(std::vector<math::TPolygon3D> &vec) const
Gets the polyhedron as a set of polygons, with the pose transformation already applied.
See also
mrpt::math::TPolygon3D,mrpt::poses::CPose3D
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inline bool isClosed() const
Returns true if the polygon is a completely closed object.
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void makeConvexPolygons()
Recomputes polygons, if necessary, so that each one is convex.
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void getCenter(mrpt::math::TPoint3D ¢er) const
Gets the center of the polyhedron.
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void updatePolygons() const
Updates the mutable list of polygons used in rendering and ray tracing.
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inline CPolyhedron()
Basic empty constructor.
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inline CPolyhedron(const std::vector<mrpt::math::TPoint3D> &vertices, const std::vector<TPolyhedronFace> &faces, bool doCheck = true)
Basic constructor with a list of vertices and another of faces, checking for correctness.
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inline void InitFromVertAndFaces(const std::vector<mrpt::math::TPoint3D> &vertices, const std::vector<TPolyhedronFace> &faces, bool doCheck = true)
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CPolyhedron(const std::vector<math::TPolygon3D> &polys)
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CPolyhedron(const std::vector<mrpt::math::TPoint3D> &vertices, const std::vector<std::vector<uint32_t>> &faces)
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~CPolyhedron() override = default
Destructor.
Public Static Functions
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template<class T>
static size_t getIntersection(const CPolyhedron::Ptr &p1, const CPolyhedron::Ptr &p2, T &container) Gets the intersection of two polyhedra, either as a set or as a matrix of intersections. Each intersection is represented by a TObject3D.
See also
mrpt::math::TObject3D
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static CPolyhedron::Ptr CreateRandomPolyhedron(double radius)
Creates a random polyhedron from the static methods.
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static CPolyhedron::Ptr CreateNoCheck(const std::vector<mrpt::math::TPoint3D> &vertices, const std::vector<TPolyhedronFace> &faces)
Creates a polyhedron without checking its correctness.
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static CPolyhedron::Ptr CreateEmpty()
Creates an empty Polyhedron.
Protected Attributes
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std::vector<mrpt::math::TPoint3D> m_Vertices
List of vertices presents in the polyhedron.
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std::vector<TPolyhedronEdge> m_Edges
List of polyhedron’s edges.
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std::vector<TPolyhedronFace> m_Faces
List of polyhedron’s faces.
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bool m_Wireframe = {false}
This flag determines whether the polyhedron will be displayed as a solid object or as a set of edges.
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mutable std::vector<mrpt::math::TPolygonWithPlane> tempPolygons
Mutable list of actual polygons, maintained for speed.
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mutable bool polygonsUpToDate = {false}
Whether the set of actual polygons is up to date or not.
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struct TPolyhedronEdge
Struct used to store a polyhedron edge. The struct consists only of two vertex indices, used to access the polyhedron vertex list.
Public Functions
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TPolyhedronEdge() = default
Default constructor. Initializes to garbage.
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inline bool operator==(const TPolyhedronEdge &e) const
Comparison against another edge. Simmetry is taken into account.
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double length(const std::vector<mrpt::math::TPoint3D> &vs) const
Given a set of vertices, computes the length of the vertex.
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~TPolyhedronEdge() = default
Destructor.
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TPolyhedronEdge() = default
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struct TPolyhedronFace
Struct used to store a polyhedron face. Consists on a set of vertex indices and a normal vector.
Public Functions
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inline TPolyhedronFace()
Fast default constructor. Initializes to garbage.
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~TPolyhedronFace() = default
Destructor.
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double area(const std::vector<mrpt::math::TPoint3D> &vertices) const
Given a set of vertices, computes the area of this face.
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void getCenter(const std::vector<mrpt::math::TPoint3D> &vertices, mrpt::math::TPoint3D &p) const
Given a set of vertices, get this face’s center.
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inline TPolyhedronFace()
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CPolyhedron::Ptr getDual() const