Some key points on Perspective Fields

1. There exists a general linear relationship between triangle points, referred to here as a Perspective Field.
2. A perspective field can be defined by four points, no three of which lie on a straight line.
3. Any point within such a field can be specified using perspective coordinates, consisting of three numerical values.
4. The perspective coordinates of a point X are the weights associated with the first three defining points of the field.
5. The general coordinates of point X are then given by a weighted average of the general coordinates of the first three defining points.
6. A similar perspective relationship also exists for triangle points on a line, referred to here as a Perspective Linear Set.

Only the underlined items are currently accessible. The remaining items are intended to be introduced in due course.

Note that:

PF-Tf1 and PF-Tf2 prove most valuable beyond the scope of Perspective Fields, especially when converting coordinates between reference triangles:

• The transformation converting coordinates from the reference triangle to another triangle is PF-Tf1.
• The transformation converting coordinates from some special triangle to the reference triangle is PF-Tf2.

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