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A model of SphericalKernel is supposed to provide some basic types
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Model of Kernel.
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Model of AlgebraicKernelForSpheres.
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Model of RootOf_2.
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Model of AlgebraicKernelForSpheres::RootForSpheres_2_3.
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Model of AlgebraicKernelForSpheres::Polynomial_1_3.
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Model of AlgebraicKernelForSpheres::PolynomialsForLines_3.
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Model of AlgebraicKernelForSpheres::PolynomialForSpheres_2_3.
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Model of AlgebraicKernelForSpheres::PolynomialsForCircles_3.
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and to define the following geometric objects
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Model of Kernel::Point_3.
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Model of Kernel::Vector_3.
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Model of Kernel::Line_3.
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Model of Kernel::Plane_3.
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Model of Kernel::Sphere_3.
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Model of Kernel::Circle_3.
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Model of SphericalKernel::LineArc_3.
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Model of SphericalKernel::CircularArc_3.
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Model of SphericalKernel::CircularArcPoint_3.
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Moreover, a model of SphericalKernel must provide predicates, constructions and other functionalities.
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Model of SphericalKernel::CompareX_3.
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Model of SphericalKernel::CompareY_3.
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Model of SphericalKernel::CompareZ_3.
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Model of SphericalKernel::CompareXY_3.
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Model of SphericalKernel::CompareXYZ_3.
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Model of SphericalKernel::CompareTheta_3.
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Model of SphericalKernel::CompareThetaZ_3.
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Model of SphericalKernel::CompareZAtTheta_3.
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Model of SphericalKernel::CompareZToRight_3.
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Model of SphericalKernel::Equal_3.
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Model of SphericalKernel::HasOn_3.
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Model of SphericalKernel::DoOverlap_3.
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Model of SphericalKernel::DoIntersect_3.
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Model of SphericalKernel::BoundedSide_3.
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Model of SphericalKernel::HasOnBoundedSide_3.
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Model of SphericalKernel::HasOnUnboundedSide_3.
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Model of SphericalKernel::IsThetaMonotone_3.
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Model of SphericalKernel::ConstructLine_3.
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Model of SphericalKernel::ConstructPlane_3.
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Model of SphericalKernel::ConstructSphere_3.
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Model of SphericalKernel::ConstructCircle_3.
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Model of SphericalKernel::ConstructLineArc_3.
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Model of SphericalKernel::ConstructCircularArc_3.
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Model of SphericalKernel::ConstructCircularArcPoint_3.
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Model of SphericalKernel::ConstructCircularMinVertex_3.
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Model of SphericalKernel::ConstructCircularMaxVertex_3.
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Model of SphericalKernel::ConstructCircularSourceVertex_3.
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Model of SphericalKernel::ConstructCircularTargetVertex_3.
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Model of SphericalKernel::ConstructBbox_3.
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Model of SphericalKernel::Intersect_3.
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Model of SphericalKernel::Split_3.
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Model of SphericalKernel::MakeThetaMonotone_3.
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Model of SphericalKernel::ComputeCircularX_3.
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Model of SphericalKernel::ComputeCircularY_3.
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Model of SphericalKernel::ComputeCircularZ_3.
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Model of SphericalKernel::ComputeApproximateSquaredLength_3.
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Model of SphericalKernel::ComputeApproximateAngle_3.
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Model of SphericalKernel::GetEquation.
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As in the Kernel concept, for each of the function objects above, there must exist a member function that requires no arguments and returns an instance of that function object. The name of the member function is the uncapitalized name of the type returned with the suffix _object appended. For example, for the function object SphericalKernel::Construct_circular_arc_3 the following member function must exist:
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For operations on a given sphere, a context sphere must be provided to the following functions:
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