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Thread: 3D rectangle construction

  1. #1

    3D rectangle construction

    How do you construct a 3D rectangle which can be modified by dragging the vertices but still maintain being a rectangle, be allowed to see the coordinate points, and to see the lengths of the different sides of the rectangle? Any thoughts?

  2. #2
    Sketchpad Developer
    Join Date
    Oct 2010

    3D Rectangle

    Hi Brett,

    First, Sketchpad has no innate 3D capability, so the required functionality for a 3D rectangle construction is not built in. If you just want to create the rectangle you describe, without directly confronting the mathematics of 3D, you should probably use a 3D geometry program or a CAD program for the purpose.

    That said, if you do want to confront the mathematics and use Sketchpad to do so, Paul Kunkel has created two packages of Sketchpad custom tools (Perpsective Tools and Solid Tools) that allow you to construct and manipulate some beautiful images of 3D shapes. (These tools construct 3D points, segments, and polygons, shade the polygons based on a light source, and remove hidden surfaces of concave 3D polyhedra. Paul has easy-to-manipulate controls for the viewing transformation and for the position of the light source. He also has tools to create shaded images of spheres, cylinders, and cones and their frustrums. Paul's tools are here: http://whistleralley.com/GSP/perspec...erspective.htm)

    Though I haven't done it, it would certainly be possible to use Paul's tools to create a rectangle such as you describe. It's easy to use Paul's tools to create the first two vertices A and B of the rectangle, along with the side joining them. The interesting part mathematically would be to use these first two vertices to determine the plane through B perpendicular to side AB. (Vertex C must lie in this plane.)

    Once you've found this plane, vertex C could be determined by creating an arbitrary 3D point and projecting it onto the required plane, or by showing the projection of the plane that must contain C on the the xy, yz, and xz planes. and using those projections to define vertex C. (The latter solution would behave more nicely when you change the positions of the first two vertices.)

    This might be a fun and interesting challenge -- or it might be more involved than you're looking for, in which case Sketchpad is not the best program for your purpose.

    Happy Sketching,

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