Discuss the Taxonomy of Projection in computer graphics, with suitable diagram. Compare and contrast Parallel & Perspective projection, in detail (i.e. with suitable examples, equations, expressions etc.). What is isometric projection? What do you understand by the term vanishing point in context of projections, in computer graphics. Obtain a Projection matrix for perspective projection of a point P(x,y,z) onto z= 5 plane, provided the center of projection is at (0,0,-10), can we find the vanishing point(s) for this projection? Justify.

Taxonomy of Projection in Computer Graphics:

Projection in computer graphics refers to the process of transforming a 3D scene onto a 2D plane, mimicking the way our eyes perceive depth and perspective in the real world. There are various types of projections, broadly categorized into two main types: Parallel Projection and Perspective Projection.

1. Parallel Projection:
   - In parallel projection, parallel lines in the 3D scene remain parallel in the 2D projection.
   - There are two common types of parallel projections: Orthographic and Oblique.
   - Orthographic projection involves projecting the 3D scene onto a 2D plane without considering perspective. All lines parallel to the viewing direction remain parallel after projection.
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