CODEWITHSUNDEEP
javageometry
user4486530
user4486530

Reputation:

Calculate intersect point between arc and line

I want to calculate the intersect point between arc and line. I have all the data for line and arc.

For line : start and and end point.
For arc : start/end point, start/end angle, radius and center point.

I have attach here one image. In this below image I have draw one arc and line where line intersect the arc.

So now I want to find the intersect point. Please give me some algorithm or idea or if any available code.

enter image description here

Upvotes: 9

Views: 11142

Answers (1)

0xJonas
0xJonas

Reputation: 289

Let's define an arc and a line:

Arc:

  • xa=X-coordinate
  • ya=Y-coordinate
  • a1=starting angle (smaller angle)
  • a2=ending angle (greater angle)
  • r=radius

Line:

  • x1=first X-coordinate
  • x2=second X-coordinate
  • y1=first Y-coordinate
  • y1=second Y-coordinate

From that you can calculate:

  • dx=x2-x1
  • dy=y2-y1
  • al=arctan(dy/dx) (Angle of the line)

The arc and the line won't intersect when al < a1 or al > a2 or, in other words, the angle of the line isn't between the angles of the arc. The equations for an intersection are as follows:

  • xa+rcos(al)=x1+cdx
  • ya+rsin(al)=y1+cdy

where c (0 < c <= 1)is the variable we're looking for. Specifically:

  • (xa+r * cos(al)-x1)/dx=c
  • (ya+r * sin(al)-y1)/dy=c

The intersection point is therefore at (x1+c * dx),(y1+c * dy)

This algorithm only works when the arc and the line have one single intersection. If the line goes through the arc two times then it won't register any intersection.

Upvotes: 4

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