CODEWITHSUNDEEP
algorithmgeometryrectangles
philm
philm

Reputation: 885

Assistance on creating algorithm for creating box around arc

I am looking for some assistance on creating an algorithm that is able to calculate a bounding box for an arc. Typically, this would be a simple problem. However, I am required to have one of the edges of the box to be the line that connects the starting point and the ending point of the arc.

I am having difficulty in developing an algorithm that is able to compute the additional two points of the rectangle.

Here is a picture of what I am attempting to calculate:

arc box

The two purple dots, I need to develop an algorithm that will determine these two locations. The green dots are the known points that can be inputs. Additionally, I do know the radius and the center of the arc.

I would need the algorithm to handle the different cases for when line AB is vertical, has a + slope, and has a - slope.

I have been considering a few directions. For example, I know that the line through point E is parallel to line AB. Since it is parallel, that means they will have the same slopes and the line from point A to the purple point is perpendicular to this line. I can then consider the intersection point of the line through E and this perpendicular line.

This method seems messy because then I would need to consider the cases for when the slope of line AB is infinite and 0. I am wondering if there is some algorithm that could account for that automatically (or not even consider the slope at all for line AB)

Upvotes: 0

Views: 239

Answers (1)

Reblochon Masque
Reblochon Masque

Reputation: 36702

enter image description here

You claim to know points A, B, C, D, E, and that the amplitude of the sustaining angle of the circular arc does not exceed 180° (semi circle).
Let P1, and P2, the two points that complement the bounding box - (in the drawing, P1 is the purple point above A, and P2 the one above B).

Using vectors:

E-C = vector perpendicular to segment AB', i/e subtract C from E; its magnitude is equal to the distance EC.
P1 = A + (E-C)
P2 = B + (E-C)

Bounding Box = Rectangle A, P1, P2, B

If you need a closer fit, you can replace vector (E-C) with vector (D-C) to place the bounding segment P1P2 tangent to D

Upvotes: 1

Related Questions