An arc-and-segment piece joins a circular arc smoothly to a straight line segment, giving curve construction both curving and straight portions in one building block. section 5.3.2
The construction is useful, but its tangent orientations matter:
- Use the implementation-ready formulas rather than treating symbolic output as the only usable result. section 5.3.2
- Handle codirected-ish and counter-oriented tangents with complementary building blocks instead of forcing one piece through every case. section 5.3.2
Solving the join
Represent the arc center as (ax1, ay1), the line point as (x2 + dx2*t2, y2 + dy2*t2), and impose perpendicularity at their intersection. Solving produces formulas for the center, parameter, and joining point.
