The plane primitive is a simple way to define an infinite flat surface. The plane is not a thin boundary or can be compared to a sheet of paper. A plane is a solid object of infinite size that divides POV-space in two parts, inside and outside the plane. The plane is specified as follows:

PLANE:
    plane
    {
        <Normal>, Distance
        [OBJECT_MODIFIERS...]
    }

The <Normal> vector defines the surface normal of the plane. A surface normal is a vector which points up from the surface at a 90 degree angle. This is followed by a float value that gives the distance along the normal that the plane is from the origin (that is only true if the normal vector has unit length; see below). For example:

  plane { <0, 1, 0>, 4 }

This is a plane where straight up is defined in the positive y-direction. The plane is 4 units in that direction away from the origin. Because most planes are defined with surface normals in the direction of an axis you will often see planes defined using the x, y or z built-in vector identifiers. The example above could be specified as:

  plane { y, 4 }

Higher order polynomial surfaces may be defined by the use of a poly shape. The syntax is

POLY:
    poly
    {
        Order, <A1, A2, A3,... An>
        [POLY_MODIFIERS...]
    }
POLY_MODIFIERS:
    sturm | OBJECT_MODIFIER

sturm : off

The cubic object is an alternate way to specify 3rd order polys. Its syntax is:

CUBIC:
    cubic
    {
        <A1, A2, A3,... A20>
        [POLY_MODIFIERS...]
    }

Also 4th order equations may be specified with the quartic object. Its syntax is:

QUARTIC:
    quartic
    {
        <A1, A2, A3,... A35>
        [POLY_MODIFIERS...]
    }

The following table shows which polynomial terms correspond to which x,y,z factors for the orders 2 to 7. Remember cubic is actually a 3rd order polynomial and quartic is 4th order.

Polynomial shapes can be used to describe a large class of shapes including the torus, the lemniscate, etc. For example, to declare a quartic surface requires that each of the coefficients (A1 ... A35) be placed in order into a single long vector of 35 terms. As an example let's define a torus the hard way. A Torus can be represented by the equation: x4 + y4 + z4 + 2 x2 y2 + 2 x2 z2 + 2 y2 z2 - 2 (r_02 + r_12) x2 + 2 (r_02 - r_12) y2 - 2 (r_02 + r_12) z2 + (r_02 - r_12)2 = 0

Where r_0 is the major radius of the torus, the distance from the hole of the donut to the middle of the ring of the donut, and r_1 is the minor radius of the torus, the distance from the middle of the ring of the donut to the outer surface. The following object declaration is for a torus having major radius 6.3 minor radius 3.5 (Making the maximum width just under 20).

  // Torus having major radius sqrt(40), minor radius sqrt(12)
  quartic {
    < 1,   0,   0,   0,   2,   0,   0,   2,   0,
   -104,   0,   0,   0,   0,   0,   0,   0,   0,
      0,   0,   1,   0,   0,   2,   0,  56,   0,
      0,   0,   0,   1,   0, -104,  0, 784 >
    sturm
  }

Poly, cubic and quartics are just like quadrics in that you do not have to understand one to use one. The file shapesq.inc has plenty of pre-defined quartics for you to play with.

Polys use highly complex computations and will not always render perfectly. If the surface is not smooth, has dropouts, or extra random pixels, try using the optional keyword sturm in the definition. This will cause a slower but more accurate calculation method to be used. Usually, but not always, this will solve the problem. If sturm does not work, try rotating or translating the shape by some small amount.

There are really so many different polynomial shapes, we cannot even begin to list or describe them all. We suggest you find a good reference or text book if you want to investigate the subject further.

The quadric object can produce shapes like paraboloids (dish shapes) and hyperboloids (saddle or hourglass shapes). It can also produce ellipsoids, spheres, cones, and cylinders but you should use the sphere, cone, and cylinder objects built into POV-Ray because they are faster than the quadric version.

Note: do not confuse "quaDRic" with "quaRTic". A quadric is a 2nd order polynomial while a quartic is 4th order.

Quadrics render much faster and are less error-prone but produce less complex objects. The syntax is:

QUADRIC:
    quadric
    {
        <A,B,C>,<D,E,F>,<G,H,I>,J
        [OBJECT_MODIFIERS...]
    }

Although the syntax actually will parse 3 vector expressions followed by a float, we traditionally have written the syntax as above where A through J are float expressions. These 10 float that define a surface of x, y, z points which satisfy the equation A x² + B y² + C z² + D xy + E xz + F yz + G x + H y + I z + J = 0

Different values of A, B, C, ... J will give different shapes. If you take any three dimensional point and use its x, y and z coordinates in the above equation the answer will be 0 if the point is on the surface of the object. The answer will be negative if the point is inside the object and positive if the point is outside the object. Here are some examples:

The easiest way to use these shapes is to include the standard file shapes.inc into your program. It contains several pre-defined quadrics and you can transform these pre-defined shapes (using translate, rotate and scale) into the ones you want. For a complete list, see the file shapes.inc.

3.4.2 Finite Patch Primitives

3.4.3 Infinite Solid Primitives

3.4.4 Isosurface Object