OpenGL Insights

150 II Rendering Techniques

projected size of a sphere with diameter equal to the length of the edge of the patch.

This solution deals effectively with the collinearity issue.

P

2

P

1

e

2

e

1

d

d

Figure 10.2. Diagram to compute

the projected sphere screen size.

To compute the projected size of the sphere

(Figure 10.2) we pick two corners sharing the

same edge, e

1

and e

2

,andcomputetheedge’s

length in world space, d. Then, we compute the

midpoint of the edge, P

1

,andanewpointabove

the centre, P

2

, displaced by the edge’s length, d.

Points P

1

and P

2

are then transformed to screen

space. The distance between the transformed

points provides the screen-space diameter of the ...