A projection flattens space onto a plane and drops one direction. The flat view of the house cannot be undone, and the determinant stays 0.
This is the plan, the top view. Height is gone.
Corner—
On plane—
det0.00
A zero row is the direction that was dropped. The determinant is 0, so you cannot undo this flatten. Lesson 06 shows the same squash. The lost direction does not come back.
3×3 projection. Read each row from left to right. A zero row drops one direction.
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Where this is used
Architects and architectural drafters draw a plan and elevations. The plan is the top view. An elevation is the front or the side. Each view drops one direction.
Mechanical drafters and CAD designers do the same for a part. The front, top, and side views sit together on one sheet.
In games, a related idea is a shadow map. A light flattens the scene onto a plane to draw a shadow. That map is not an architectural plan.
In cartography, a related idea is a map projection. A cartographer flattens the Earth onto a sheet. Information is lost, but the matrix is not this one.
Common mistakes
The lost coordinate does not come back. A determinant of 0 means this flatten has no inverse.
A projection is not a perspective drawing. Perspective divides by w. This view only drops a direction.
Tilting the plane still leaves the determinant at 0.
A shadow map and a map projection are related ideas. They are not this matrix.