Quadric curve skeletal element. More...
#include <blobtree.h>
Public Member Functions | |
| TreeQuadricCurve (const QuadricCurve &, BlendCompact *) | |
| Creates a quadric polynomial curve skeletal element. More... | |
| virtual | ~TreeQuadricCurve () |
| Destroys a curve. | |
| virtual TreeNode * | Copy () const |
| Creates a deep copy of curve element. | |
| int | Memory () const |
| Compute the size of a node. | |
| double | Intensity (const Vector &) const |
| Compute the intensity at a given point. More... | |
 Public Member Functions inherited from TreeNormal | |
| TreeNormal (BlendCompact *=nullptr) | |
| Creates a skeletal element given a blending function. | |
| virtual | ~TreeNormal () |
| Destroys a skeletal element. | |
| virtual Vector | Gradient (const Vector &) const |
| Compute the gradient at a given point. More... | |
| virtual void | IntensityGradient (const Vector &, double &, Vector &) const |
| Compute the field value and the gradient of the field function at a given point in space. More... | |
| virtual double | K (const Segment &) const |
| Compute the Lipschitz constant on a segment. More... | |
| virtual double | K (const RayStep &) const |
| Compute the Lipschitz constant on a segment. More... | |
| virtual double | K (const Sphere &) const |
| Compute the Lipschitz constant inside a sphere. More... | |
| Public Member Functions inherited from TreeElement | |
| TreeElement (BlendCompact *=nullptr) | |
| Creates a new element given a blending function. | |
| virtual | ~TreeElement () |
| Destroys an element. More... | |
| double | K () const |
| Returns the Lipschitz constant of the element. More... | |
| double | K (const Box &) const |
| Returns a local Lipschitz constant within a box domain. More... | |
| double | K (const Ray &) const |
| Returns a local Lipschitz constant along a ray. More... | |
| TreeNode * | Cut (const Box &) const |
| Cuts the node to simplify its structure inside a box. More... | |
| Public Member Functions inherited from TreeNode | |
| TreeNode () | |
| Create a virtual node of the Blob-Tree structure. | |
| virtual | ~TreeNode () |
| Destroys a node. | |
| virtual TreeNode * | Blend (TreeNode *) |
| Insert a blending node that blends the old and the new sub-tree together. More... | |
| virtual TreeNode * | Union (TreeNode *) |
| Insert a union node that unions the old and the new sub-tree together. More... | |
| virtual TreeNode * | Difference (TreeNode *) |
| Insert a difference node. More... | |
| virtual TreeNode * | Translate (const Vector &) |
| Insert a translation node. More... | |
| virtual TreeNode * | Rotate (const Matrix &) |
| Insert a rotation node. More... | |
| virtual TreeNode * | Scale (const Vector &) |
| Insert a scaling node. More... | |
| Box | GetBox () const |
| Return the bounding box of the node. | |
| virtual void | SetThreshold (const double &) |
| Set the threshold value. More... | |
| virtual Color | GetMaterial (const Vector &, const Vector &=Vector::Null) const |
| Gets the color of a node at a point. More... | |
| virtual int | Nodes () const |
| Compute the number of nodes of the sub-tree. | |
| virtual int | Depth () const |
| Compute the dpeth of the sub-tree. | |
| virtual Vector | Dichotomy (Vector, Vector, double, double, double, const double &=1.0e-4) |
| Compute the intersection between the implicit surface and a segment. More... | |
Protected Member Functions | |
| Vector | Normal (const Vector &) const |
| Compute the distance vector between a point in space and the curve. More... | |
| double | R (const Vector &) const |
| Compute the squared distance between a point in space and the quadric curve. More... | |
Protected Attributes | |
| QuadricCurve | c |
| Quadric polynomials defining the curve. | |
| Quadric | xyz |
| Quadric constant coefficients used to speed-up ray-tracing. | |
| Vector | b |
| End vertices of the curve. | |
| Protected Attributes inherited from TreeNode | |
| Box | box = Box::Null |
| Bounding box of the node. | |
| double | T = 0.5 |
| Threshold value. | |
Additional Inherited Members | |
| Static Protected Attributes inherited from TreeNode | |
| static const double | Epsilon = 1e-6 |
| Epsilon value for gradient computation. | |
Detailed Description
Quadric curve skeletal element.
The evaluation of the field function is computationally less intensive than the TreeCubicCurve primitive: the computation of the distance to the skeleton requires finding the roots of a cubic polynomial only.
,
Constructor & Destructor Documentation
◆ TreeQuadricCurve()
| TreeQuadricCurve::TreeQuadricCurve | ( | const QuadricCurve & | c, |
| BlendCompact * | blend | ||
| ) |
Creates a quadric polynomial curve skeletal element.
- Parameters
-
c Quadric curve. blend Falloff function.
Member Function Documentation
◆ Intensity()
|
virtual |
◆ Normal()
Compute the distance vector between a point in space and the curve.
This function computes the projection of a point p onto the curve by minimizing the distance function along the curve, expressed as a cubic. As most of the coefficients are constant, they are pre-processed in the constructor.
Cumulative speed-ups come from pre-processing constant coefficients and invoking an inline normalized cubic solver.
- Parameters
-
p Point.
Implements TreeNormal.
◆ R()
|
protectedvirtual |
Compute the squared distance between a point in space and the quadric curve.
This function computes the projection of a point p onto the curve by minimizing the distance function along the curve, expressed as a cubic polynomial. As most of the coefficients of this cubic polynomial are constant, they are pre-processed in the constructor.
- Parameters
-
p Point.
Reimplemented from TreeNormal.
