General Quadric Surface
- Author:
- Dr. Doug Davis, 3D
- Topic:
- Conic Sections, Intersection, Surface
Description
This applet allows you to explore general quadric surfaces. The equation
describes a quadric surface. All of the coefficients can be adjusted to investigate there impact.
A selection of named surfaces can be chosen that resets the coefficients for those surfaces. Most of the terms get set to 0 for these surfaces.
The view can be rotated, scaled and translated to better see the shapes.
To help visualize the shape, slices parallel to the primary planes can be shown. The position of the plane can be adjusted with sliders. The in-plane equation of the intersection is also shown.
Special Cases
The quadric surfaces equations can be modified so that the coefficients for many of the surfaces can represent scale. Basically by substituting for the intersection with the axis will often be equal to . The applet below shows some of the surfaces with equations in the new form. Note that often for proper scaling should be 0 or 1.
Quadric Surfaces
2 Dimensional Curves
To help visualize the three-dimensional shapes a review of two-dimensional curves is helpful. The applet below shows quadratic curves related to the quadric surfaces above. So by fixing one of the coordinate values to a constant the curve in that plane may be recognized as one of the curves below. This will be a curve in a plane perpendicular to the constant value axis at the constant value.