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Line of Sight Demo: Cylinder, Prism, and Pythagorean Theorem

Line of Sight Demo: Cylinder, Prism, and Pythagorean Theorem
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2018-05-17 03:23
Coordinate GeometrySolid GeometryTransformationGeometric ConstructionSlider Animation
In collections Mathematics of Computer Graphics
① This interactive GeoGebra example demonstrates how a line of sight from a camera is blocked by a cylinder and a prism, and uses the Pythagorean theorem to compute sight distances. ② Core math concepts include the Pythagorean theorem, median lines, solid geometry of cylinders and prisms, and dilation transformations. ③ Construction highlights: using GeoGebra commands Polygon, Textfield, PointIn, Line, and Intersect; objects include camera, cylinder C, prism poly1, radii r1-r4, points P, C1, A, B, dynamic texts text1-text12, and a button for controlling the demo. ④ Suitable for high school or early college students to explore spatial reasoning, occlusion, and distance calculations in 3D, as well as interactive geometric construction techniques.

GeoGebra Commands & Parameters

  1. Polygon(R1, R4, R2, R3) → poly1, r1, r4, r2, r3
  2. Textfield(r) → inputBox4
  3. PointIn(poly1) → P
  4. Line(C1, P) → e
  5. Intersect(e, d) → A, B
  6. Textfield(C) → InputBox1

AI Drawing Prompt Reference

Create a 3D scene with a cylinder and a prism, plus a camera viewpoint. A line of sight from the camera is blocked by the cylinder and prism, intersecting the prism surface at two points. Place a random point inside the prism and connect it to the camera with a line. Use a slider to adjust the cylinder radius, and display multiple dynamic texts labeling sight distances, intersection positions, and radius values. Include an input box to adjust the camera position. The scene demonstrates line-of-sight occlusion and distance calculation using the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.