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Egwald Mathematics: Geometry - 3D House


Elmer G. Wiens

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Painters and computer programmers struggle with perspective to depict 3-dimensional figures on a 2-dimensional surface. On this page you can view the house from different points-of-view, by changing three parameters, theta, phi, and rho. These three parameters are the spherical coordinates of the point P, the point-of-view of the observer.
rho = distance from the origin to P
theta = the angle between the x-axis and the projection
          of the line from the origin to P onto the x-y plane
phi = the angle from the z-axis to the point-of-view line
The three dimensional co-ordinate system consisting of the x, y, and z axis is drawn in black. The point-of-view of the observer, P, is drawn in blue. The perpendicular from P to the x-y plane, and the projection of P on the x-y plane, are in red.
The house is displayed from the point-of-view of the observer. The x-axis (red), y-axis (green), and z-axis (yellow) spin with the house as the point-of-view changes.

Parameters of the Point-of-View
angle with the x-axis: theta [-pi, pi]
angle with the z-axis: phi [0, pi]
distance from the origin: rho [60, 100]

Change the parameters, the angles are in radians, and click "Graph House" to view the house from a different perspective.


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