Considering the tool as an Orthographic camera

• Static collision detection (the tool is still orits motion between 2 times steps is not considered)

• PO is the tool fixed point,

• P is the tool extremity position.

• Camera near plane: N = PO

• far plane: F = P

• Considering the tool section as a square gives L, R, T, and B

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When the tool doesn’t move, or wen we neglect the tool movement, we can easily approximate its geometry by an orthographic viewing volume.

We only have to define the point of view on the axe of the tool and put near and far planes according to the extremities of the tool.

If we consider that a tool section is a square we directly have the other planes.

Running the geometrical step of the rendering process gives us the facets colliding the tool.