REMARK: Endpoints , inflection point and are user defined. The tangent angle at both endpoints can be | obtained either from three point circular arc approximation around the endpoints or the user defines it. Let represent the | coordinate of a point. | INPUT: , , , . | OUTPUT: , , , LAC segment. | Begin | Step 1. Set , where is the center of circle, is radius and represents angle. | Step 2. Identify unit tangent vector, and set . | Step 3. Calculate directional angle, . | Step 4. Solve simultaneous equations , where to get position of second control point . | Step 5. If , then , | else ; . | If , then ; , | else ; . | Step 6. Translate , rotate triangle such that for ; for . | If or , then reflect the triangle through -axis. | Step 7. Compute . | Step 8. If , then , | else . | Step 9. Identify bound of . If , then ; , | else if , then ; , | else ; . | Step 10. Set tolerance ; | iteration number . | Step 11. Calculate using Bisection method. | Step 12. Determine scaling factor, . | Step 13. Scale to the curve and transform inversely the triangle to its original position. | Step 14. Construct LAC segment using (2). | Step 15. OUTPUT (, , , LAC segment). | End |
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