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libgenua
Basic Geometry, Numerical Algorithms and Interfaces
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libgenua
Basic Geometry, Numerical Algorithms and Interfaces
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Triangular face.
A Face always belongs to a Triangulation (which can be retrieved from any Face object by Face::surface()), to which it stores a pointer. When copying collections of Faces, remember that their parent triangulation must exist, otherwise, calls to some member functions of Face will lead to assertion failures.
Face provides access to the indices of its vertices by Face::vertex(), which you might call with integers of using the VertexId enum.
uint vr, vg, vb; Face f; vr = f.vertex(1); vr = f.vertex(v_red); // equivalent vg = f.vertex(2); vg = f.vertex(v_green); // equivalent
For each set of three vertices, only two different vertex orderings (red,green,blue) are possible, allowing two different normal directions. This restriction is necessary to define a unique face ordering. Thus, if you define a Face(&tg, 45, 61, 2), it is exactly the same as Face(&tg, 2, 45, 61). (Actually, the second variant is stored in both cases.) Normal direction is never changed by this reordering.
Face has moderate size, normally 16 bytes.
#include <edgeface.h>
Public Member Functions | |
| Face () | |
| empty construction | |
| Face (const Triangulation *parent, uint p1, uint p2, uint p3) | |
| definition by vertices | |
| Face (const Triangulation *parent, const Edge &ed1, const Edge &ed2, const Edge &ed3) | |
| definition by edges | |
| virtual | ~Face () |
| virtual destruction | |
| bool | valid () const |
| check validity | |
| bool | operator== (const Face &a) const |
| equality | |
| bool | operator!= (const Face &a) const |
| inequality | |
| bool | operator< (const Face &a) const |
| comparison | |
| uint | vertex (uint i) const |
| access | |
| void | getVertices (uint vi[3]) const |
| copy vertex indices into array | |
| const uint * | vertices () const |
| access vertex index pointer | |
| uint * | vertices () |
| access vertex index pointer | |
| void | getEdges (Edge edg[3]) const |
| copies edges into array | |
| Edge | edge (uint i) const |
| access edge | |
| bool | hasEdge (const Edge &e) const |
| check if edge is present in this face | |
| uint | opposed (const Edge &e) const |
| find vertex opposed to edge e | |
| Edge | opposed (uint i) const |
| find edge opposed to vertex i | |
| uint | neighbors (Face f[3]) const |
| find the neighbor faces connected to edges | |
| const Triangulation * | surface () const |
| access | |
| void | setSurface (const Triangulation *parent) |
| change reference | |
| Vct3 | eval (Real xi, Real eta) const |
| evaluate parameters | |
| Real | eval (const Vector &u, Real xi, Real eta) const |
| evaluate scalar field over triangle | |
| Vct3 | normal () const |
| compute normal | |
| Vct3 | center () const |
| compute center | |
| Vct3 | project (const Vct3 &pt) const |
| project, return parameters and signed distance to projection | |
| Vct3 | pierce (const Edge &e) const |
| Find the point where an edge would pierce this face, return the projection parameter (u,v,t). More... | |
| SMatrix< 3, 3 > | trafo () const |
| return transformation matrix for local coordinate system | |
| void | gradient (Mtx33 &gm) const |
| Gradient. More... | |
| Vct3 | gradient (const Vector &x) const |
| computes the gradient of global x on this triangle | |
| CpxVct3 | gradient (const CpxVector &x) const |
| computes the gradient of global x on this triangle | |
| Real | corner (uint gv) const |
| compute corner angle for (global) vertex gv | |
| Real | solidAngle (uint idx) const |
| compute solid angle associated with vertex idx | |
| Real | solidAngle (uint idx, const Vct3 &a) const |
| compute solid angle associated with vertex idx, for normal a | |
| Real | quality () const |
| triangle quality | |
| void | orderCanonical () |
| make ordering canonical | |
| void | reverse () |
| reverse normal | |
| void | replace (uint vold, uint vnew) |
| replace index | |
| uint | inside (const BndBox &bb) const |
| return how many of this face's vertices are inside the box | |
| Real | minDistance (const Vct3 &pt, Vct2 &foot) const |
| return minimum signed distance of pt to this triangle, set foot point parameter | |
Protected Attributes | |
| const Triangulation * | srf |
| parent object | |
| uint | v [3] |
| vertex indices | |
| void Face::gradient | ( | Mtx33 & | gm | ) | const |
Gradient.
Computes the matrix relating a scalar property associated to the vertices to its gradient in global 3D coordinates.
Find the point where an edge would pierce this face, return the projection parameter (u,v,t).
The point is inside the face if 0<u,v,w<1 where w = 1-u-v. (t) is the edge parameter.
1.8.5
