5.3.2 Quadric

The syntax of the quadric object is:

QUADRIC:
  quadric { COEFF1, COEFF2, COEFF3, COEFF4 [OBJECT_MODIFIERS] }

See also:

• [pov:6.5.3.3]Quadric

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

$$\{\langle X,Y,Z\rangle : a_X\,X^2+a_Y\,Y^2+a_Z\,Z^2 + b_Z\,XY + b_Y\,XZ+b_X\,YZ +$$

$$\quad+ c_X\,X+c_Y\,Y+c_Z\,Z+d \leq 0 \}$$

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