This applet allows you to explore general quadric surfaces. The equation[br][math]a_{x2}\cdot x^2+a_{y2}\cdot y^2+a_{z2}\cdot z^2+a_{xy}\cdot x\cdot y+a_{yz}\cdot y\cdot z+a_{zx}\cdot z\cdot x+a_x\cdot x+a_y\cdot y+a_z\cdot z=a_0[/math] [br]describes a quadric surface. All of the coefficients can be adjusted to investigate there impact.[br]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.[br]The view can be rotated, scaled and translated to better see the shapes.[br]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.

The quadric surfaces equations can be modified so that the coefficients for many of the surfaces can represent scale. Basically by substituting [math]\frac{x^2}{a^2}[/math] for [math]a_{x2}\cdot x^2[/math] the intersection with the [math]x[/math] axis will often be equal to [math]a[/math]. The applet below shows some of the surfaces with equations in the new form. Note that often for proper scaling [math]d[/math] should be 0 or 1.

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.