CGAL 4.7 - 3D Spherical Geometry Kernel: Class and Concept List

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 3D Spherical Geometry Kernel

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Class and Concept List
Here is the list of all concepts and classes of this package. Classes are inside the namespace CGAL. Concepts are in the global namespace.
[detail level 12]

CGAL |
Algebraic_kernel_for_spheres_2_3 |
Circular_arc_3 |
Circular_arc_point_3 |
Exact_spherical_kernel_3 | A typedef to a spherical kernel that provides both exact geometric predicates and exact geometric constructions
Line_arc_3 |
Polynomial_1_3 |
Polynomial_for_spheres_2_3 |
Polynomials_for_lines_3 |
Root_for_spheres_2_3 |
Spherical_kernel_3 |
AlgebraicKernelForSpheres | The `AlgebraicKernelForSpheres` concept is meant to provide the curved kernel with all the algebraic functionalities required for the manipulation of spheres, circles, and circular arcs in 3D
CompareX |
CompareXY |
CompareXYZ |
CompareY |
CompareZ |
ConstructPolynomial_1_3 |
ConstructPolynomialForSpheres_2_3 |
ConstructPolynomialsForLines_3 |
Polynomial_1_3 | Concept to represent trivariate polynomials of degree 1 whose coefficients are of a type that is a model of the concept `RingNumberType`
PolynomialForSpheres_2_3 | Concept to represent trivariate polynomials of degree up to 2 capable of storing equations of spheres, whose center's coordinates, as well as the square of the radius, are of a type that is a model of the concept `FieldNumberType`
PolynomialsForCircles_3 | Concept to represent a system of polynomials on `FieldNumberType` capable of storing equations of circles
PolynomialsForLines_3 | Concept to represent a system of polynomials on `FieldNumberType` capable of storing equations of lines
RootForSpheres_2_3 | Concept to represent the roots of a system of three equations of degree 2 in three variables `x`, `y` and `z` that are models of concept `AlgebraicKernelForSpheres::PolynomialForSpheres_2_3`
SignAt |
Solve |
XCriticalPoints |
YCriticalPoints |
ZCriticalPoints |
SphericalKernel |
BoundedSide_3 |
CircularArc_3 | Concept for arcs of circles
CircularArcPoint_3 | Concept for points on spheres, circles, circular arcs or line arcs
CompareTheta_3 |
CompareThetaZ_3 |
CompareX_3 |
CompareXY_3 |
CompareXYZ_3 |
CompareY_3 |
CompareZ_3 |
CompareZAtTheta_3 |
CompareZToRight_3 |
ComputeApproximateAngle_3 |
ComputeApproximateSquaredLength_3 |
ComputeCircularX_3 |
ComputeCircularY_3 |
ComputeCircularZ_3 |
ConstructBbox_3 |
ConstructCircle_3 |
ConstructCircularArc_3 | The circular arc constructed from a circle, a source, and a target, is defined as the set of points of the circle that lie between the source `p1` and the target `p2`, when traversing the circle counterclockwise seen from the side of the plane of the circle pointed by its positive normal vectors
ConstructCircularArcPoint_3 |
ConstructCircularMaxVertex_3 |
ConstructCircularMinVertex_3 |
ConstructCircularSourceVertex_3 |
ConstructCircularTargetVertex_3 |
ConstructLine_3 |
ConstructLineArc_3 |
ConstructPlane_3 |
ConstructSphere_3 |
DoIntersect_3 | Testing whether two curves or surfaces intersect
DoOverlap_3 |
Equal_3 | Testing equality between objects
GetEquation |
HasOn_3 |
HasOnBoundedSide_3 |
HasOnUnboundedSide_3 |
Intersect_3 |
IsThetaMonotone_3 |
LineArc_3 | Concept for line segments supported by a line that is a model of `Kernel::Line_3`, and whose endpoints are models of the `SphericalKernel::CircularArcPoint_3` concept
MakeThetaMonotone_3 |
Split_3 |