Surfaces in space

Content: This page contains an applet for visualising surfaces in space and instructions for its use.

Applet

Theory

Analysis for Computer Scientists, Chapter 15

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Drawing a surface

As can be seen from the screenshot, the surface must be defined in the field f(x,y)= by a functional expression in the variables x and y. Detailed information on the syntax can be found here. With the slider Number of grid points it is specified how many points are used to graphically approximate the surface. The (rectangular) domain of the function is defined in the fields Interval x and Interval y.

Surface options

In addition to the number of grid points, the tab Surface options allows you to adjust the image. The selection box Surface determines whether the surface is drawn as a (transparent) wireframe or with texture (a mixed option is also available). The Filling options determine how the triangles from which the surface is constructed are coloured. The option Simple fills the entire triangle with the colour of one of its vertices. If the option Interpolate is selected the colour is interpolated between the colours of the vertices. The option Colour admits additional modifications that influence the colour of the surface. If the option z is selected the colour changes only in z-direction. With the option xy the colour changes only in x- and y-directions. The option xyz changes the colour in all directions. The option Front and Back has the effect of drawing the surface with only two colours, one for the front side and one for the back. In addition, the field Rendering options allows one to choose between high image quality or fast display.

Projection

The tab Projection allows you to choose the type of projection. With the options Perspective and Parallel projection you can select between these two types of projection. If Perspective is selected the distance of the camera from the surface can be adjusted by the minus and plus buttons. The selection box Projection plane allows one to specify a parallel projection onto one of the coordinate planes. The button Reset restores the default values.

Surface rotation

By moving the mouse while pressing the left mouse button the surface can be rotated.

Scaling the axes, boxes, and labels

The tab Axes allows one to control the scaling of the axes. Depending on the chosen option, the axes can be scaled jointly or independently. In the selection box Axes model it can be specified whether a box with or without labels is displayed.

Partial derivatives

The tab Partial derivatives allows one to visualise partial derivatives, directional derivatives and tangent planes. If the option Partial derivative is selected, clicking on the red grid in the xy-plane selects a point in that plane. At this point both tangents are drawn. To visualise a directional derivative, two points have to be selected from the xy-plane. The first click determines the point at which the directional derivative is to be computed, while the second click determines the direction. If the option Tangent plane is selected a single click determines the point at which the tangent plane is shown.

Questions

If you have further questions or comments, or if you found a bug, please send us an e-mail.

Financially supported by

University of Innsbruck: New Media and Learning Technologies
Austrian Federal Ministry of Education, Science and Research

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