In this appendix we will study several families of so-called quadratic surfaces, namely surfaces z = f(x, y) which are defined by equations of the type. Ax2 + By2 +. Spheres and cones are examples of quadrics. The quadric surfaces of RenderMan are surfaces of revolution in which a finite curve in two dimensions is swept in. Quadric Surfaces - Traces. Traces are cross sections parallel to a plane. The xy trace is found by setting z = 0. The yz trace is found by setting x = 0. The xz trace.


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Quadric surfaces of Two Sheets Here is the equation of a hyperboloid of two sheets. The variable with the positive in front of it will give the axis along which the graph is centered. Notice that the only difference between the hyperboloid of one sheet and the hyperboloid of two sheets is quadric surfaces signs in front of the variables.

They are exactly the opposite signs.


Elliptic Paraboloid Here is the equation of an elliptic paraboloid. Here is a sketch of a typical elliptic paraboloid. Quadric surfaces Paraboloid Here is the equation of a hyperbolic paraboloid.


Here are a couple of quick sketches of this surface. The sketch on the left has the standard set of axes but it quadric surfaces difficult to see the numbers on the axis.

Quadric - Wikipedia

In most sketches that actually involve numbers on the axis system we will give both sketches to help get a feel for what the sketch looks like. The basic quadric quadric surfaces are described quadric surfaces the following equations, where A, B, and C are constants.

Rather than memorize the equations, you should learn how to examine cross sections to figure out what surface a given equation represents. Using This Gallery In this gallery you'll find interactive pictures of the quadric surfaces.

Quadratic Surface

You can see what the cross sections look like, and also see how various coefficients can quadric surfaces how they look.

These pictures all include "sliders," like the following two examples. The picture on the left shows a sphere with an adjustable radius; click and drag the blue dot to change it.

The picture on the quadric surfaces shows you the various cross sections of the sphere.

Quadratic Surface -- from Wolfram MathWorld

Click and drag the blue dots to adjust the chosen values for x, y, and quadric surfaces. You can see what the cross sections look like, and also see how various coefficients can affect how they look. The first picture below shows a sphere with an adjustable radius; click and drag quadric surfaces blue slider to change it.

You can rotate the sphere by grabbing and dragging. You can also zoom in or out using the scroll wheel on quadric surfaces mouse or the equivalent touch motion. Reset view There are additional controls quadric surfaces the bottom of the picture that determine how the surface is shown: