Why Another Clipper

Cohen-Sutherland is restricted to axis-aligned rectangles. Cyrus-Beck clips a line against any convex polygon (including the rectangular window) by working in parametric form.

Parametric Setup

Represent the line as P(t) = P0 + t * (P1 - P0), with t in [0, 1] giving the visible segment of an unclipped line.

For each edge i of the convex window with an outward (or inward, with consistent sign) normal N_i and a point F_i on the edge: N_i . (P(t) - F_i) = 0 -> t_i = (N_i . (F_i - P0)) / (N_i . D), where D = P1 - P0.

Classification (using inward normals N_i)

• If N_i . D > 0: the line is going from outside to inside as t increases -> PE (potentially entering).
• If N_i . D < 0: from inside to outside -> PL (potentially leaving).
• If N_i . D = 0: parallel; check sign of N_i . (F_i - P0): if negative, line is on outside side of this edge -> reject; else this edge does not constrain.

Compute t_E and t_L

• t_E = max(0, max(t_i over all PE edges)).
• t_L = min(1, min(t_i over all PL edges)).

If t_E > t_L: the line misses the window (reject). Else clipped segment is from P(t_E) to P(t_L).

Worked Sketch

Convex pentagon window with edges E1..E5. Line from P0(-3, 0) to P1(7, 5). Compute D = (10, 5). For each edge, compute t_i and tag as PE or PL. Suppose t_E = 0.3 and t_L = 0.85; then visible segment runs from P(0.3) = (0, 1.5) to P(0.85) = (5.5, 4.25).

Comparison

Liang-Barsky Note

Liang-Barsky is the special case of Cyrus-Beck for axis-aligned rectangles, written with simple inequalities x_min <= x <= x_max etc. It is generally faster than Cohen-Sutherland for non-trivial cases because of fewer branches.