I haven't written this type of code, but my approach would be to write a function that converges on the approximation of where the bezier curve and the line segment intersect.
Here are links to code to get you started
Bezier Code: http://blitzbasic.com/codearcs/codearcs.php?code=170
Line-Line Intersect: http://blitzbasic.com/codearcs/codearcs.php?code=1202
For example:
Using only 10 points to plot your bezier curve, test each line segment between the ten points until you determine if the bezier and line segment intersect using line-line intersect code.
If the lines intersect you know approximately where they intersect. This may be good enough at this rough scale, again depending on how accurate you need to be.
Otherwise, increase the number of segments in your bezier to 100 points, 1000 points (and so on...) and continue looking for line-line intersects until you zero in on the most accurate coordinates.
Good Luck,
Andy
Here are links to code to get you started
Bezier Code: http://blitzbasic.com/codearcs/codearcs.php?code=170
Line-Line Intersect: http://blitzbasic.com/codearcs/codearcs.php?code=1202
For example:
Using only 10 points to plot your bezier curve, test each line segment between the ten points until you determine if the bezier and line segment intersect using line-line intersect code.
If the lines intersect you know approximately where they intersect. This may be good enough at this rough scale, again depending on how accurate you need to be.
Otherwise, increase the number of segments in your bezier to 100 points, 1000 points (and so on...) and continue looking for line-line intersects until you zero in on the most accurate coordinates.
Good Luck,
Andy