5.3.2 Quadric

The syntax of the quadric object is:
QUADRIC:
  quadric { COEFF1, COEFF2, COEFF3, COEFF4 [OBJECT_MODIFIERS] }
See also: It describes a quadric (surface given by a quadratic polynomial in the variables $ X$, $ Y$ and $ Z$) with coefficients COEFF1( $ =\langle a_X,a_Y,a_Z\rangle$) of the homogeneous quadratic part, coefficients COEFF2( $ =\langle b_Z,b_Y,b_X\rangle$) of the inhomogeneous quadratic part, coefficients COEFF3( $ =\langle c_X,c_Y,c_Z\rangle$) of the homogeneous linear part and constant coefficient COEFF4($ =d$) given by

$\displaystyle \{\langle X,Y,Z\rangle$ $\displaystyle : a_X\,X^2+a_Y\,Y^2+a_Z\,Z^2 + b_Z\,XY + b_Y\,XZ+b_X\,YZ +$    
  $\displaystyle \quad+ c_X\,X+c_Y\,Y+c_Z\,Z+d \leq 0 \}$    

Note the unusual order of COEFF2! As particular cases we get ellipsoids, paraboloids, hyperboloids, and the degenerated cases of cylinders, double cones, etc. ...

Figure: Hyperboloids
Image /home/andreas/tex/Books/computer-graphics/img//obj-hyperboloid.png

Andreas Kriegl 2003-07-23