gifRange Adjust / Truncate Overview

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The Range Adjust mechanism targets spherical coordinates within a specified range of Theta. You specify a Min/Max range for Theta, and a 'New' Theta value. Vertices whose Theta is greater than Min and less than Max are adjusted to the New value.

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A = 109.49915455
B = 107.20304672
MIN = 100
MAX = 113
NEW = 105

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If Truncate is checked, the sphere is truncated either above or below 'New'. If you intend to generate a Dual manifold, you must check ‘Truncate for 'Generate Dual' ’. This will ensure that the Dual sits flat on the truncation plane by inserting special vertices in the Primal manifold; these vertices are invisible to the user and maintain duality within the system.

The ‘Radius’ and ‘Trunc Y’ fields show the length of the radius and its Y value at the intersection of the current envelope. Obviously these values will depend on the extents and shape of the envelope. In the diagram below, the white arrow is a ray whose direction vector is formed by the spherical coordinate with theta value 'New'. Envelopes 1, 2 and 3 produce three different Y values for the given theta at the envelope intersections:

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IMPORTANT: All Range Adjust / Truncate operations must be performed on envelopes that conform to surfaces of revolution about the Y axis. This means if the current envelope is a SuperEllipsoid the East-West exponent must first be set to 2.0. Likewise, if using an Ellipsoid the X extent must equal the Z extent. You can change the extents and exponents after truncation. Further, you can select any envelope type and the truncation plane will remain in effect.

If the current envelope does not conform to a surface of revolution, Geodesica will ask you to change it when you click the Truncate png button.

Example

1. Switch to the front camera by right-clicking in the OpenGL view and choosing ‘Front’ from the pop-up menu. Create a 5V icosahedron, Class I Method 1 sphere. This sphere has no truncation plane at the equator (horizontal red line) but may truncated by adjusting vertices within a specified range so that they all have the same Theta value. In the screenshot below, it is desired to form a truncation plane using the vertices that lie on the wavy red line encircling the sphere.

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2. Select the Pick Element tool png with the Pick Vertex tool png on the Toolbar. It is desired to truncate the sphere using the Theta value of the vertex in the yellow circle. Click on this vertex; the Theta value given in the Vertex Editor is: 109.49915455.

Now click on the vertex in the red circle. The Theta value given in the Vertex Editor is: 107.20304672.

3. Bring up the Rane Adjust / Truncate window by clicking the png button on the Toolbar and enter the following values for Min, Max and New:

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Ensure that ‘Project adjustment’ is checked and click ‘Apply’. All vertices whose Theta lies within the specified range of Min and Max are adjusted to the New value.

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4. It is now a simple matter to truncate the sphere. Check the Truncate button and click ‘Truncate below 'New' value’. The sphere is truncated.

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5. Bring up the Envelopes window by clicking the png button on the Toolbar and change the envelope to a SuperEllipse of Revolution. The subdivision is re-projected but the truncation plane remains the same:

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The above rule holds true for any envelope type.

After performing a Range / Adjust Truncate, an internal check is made to ensure that all truncation plane radii have the same Y values, Theta values and radii.