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Scalar function F(x,y,z). Inside < 0, surface = 0, outside > 0. All quadratic trivariate functions are given by

or

or

or


Sphere
at center with radius :




Cylinder
along the axis around with radius :




Cone
apex at , opening along the axis with an angle of




Quadric Transformation
Given a point on the surface of a quadric :

we apply a transformation to :

we obtain
(M^{-1} x')^T Q M^{-1} x' = 0


Thus, the quadric after application of the transformation is:


Ray / Quadric Intersections




Has 0, 1, or 2 real solutions.