Currently, integrated Arcs take the center of the arc and weigh it by it's arc length. This is incorrect.
The new integrations will be for disk and arc.
Arc integration will be approximately arc.position(-angle/4) + arc.position(+angle/4) [or the quarter positions to the left and right, where the horizontal components will cancel] and then multiply by arc length (weight). A more exact formula may exist, e.g. sine and cosine have straightforward derivatives.
Disk integration is more complicated, definition-dependent, and of questionable utility.
mattrdowney
commented
5 years ago
Currently, integrated Arcs take the center of the arc and weigh it by it's arc length. This is incorrect.
The new integrations will be for disk and arc.
Arc integration will be approximately arc.position(-angle/4) + arc.position(+angle/4) [or the quarter positions to the left and right, where the horizontal components will cancel] and then multiply by arc length (weight). A more exact formula may exist, e.g. sine and cosine have straightforward derivatives.
Disk integration is more complicated, definition-dependent, and of questionable utility.