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The Meaning of 'startParam' and 'endParam' Parameters in Conic Sections
skylark_1003
Member Posts: 1 EDU
I would like to understand how startParam and endParam determine the start and end points of a conic section.
As shown in the diagram, when defining a conic segment, we need three points: A (start), B (end), and C (control). Point M is the midpoint of AB, and the ratio MD/MC is equal to rho. When the conic is clipped, two additional parameters, startParam and endParam, define the start and end points.
I have experimented and found that in the case of a parabola (where rho = 0.5), for example, point E is the end point, and the ratio AF/AB equals to endParam (with EF being parallel to CM). However, this does not seem to be the case for elliptical arcs and hyperbolas (where rho ≠ 0.5).
AF/AB = 0.75
rho=0.5:
endParam=0.75rho=0.8:
endParam= 0.8931498239186069rho=0.3:
endParam=0.6887505003980625
My previous statement may have been incorrect. If you could point it out and tell me the significance of startParam and endParam parameters, I would greatly appreciate it.
Answers
I'm not exactly sure where you're seeing these params listed, but it sounds to me like it's for "trimming" the conic ends. In your diagram the untrimmed conics seems like they would all end at B. The parameter is like a percentage along the curve from 0 to 1, so a param of 0.75 means that end point is 75% along the untrimmed conic. Just a guess that's what this is about.