O.K., if you need some math... Let's start. If an arc of a circle begins at point M1 (R 0) and goes up to point M4 (R*cos(f), R*sin(f)). If f<pi/2, you may use one cubic Bezier curve. Otherwise you should draw additional curves. You should find two control points: M2 and M3. M2 (R, h) and M3 (R*cos(f)+h*sin(f), R*sin(f)-h*cos(f)). Here you should calculated h. h=(4/3)*R*tg(f/4) or, what is the same, h=(4/3)*R*(1-cos(f/2))/sin(f/2). Assume, that angle f is positive, if goes counterclockwise. If you have an ellipse instead of a circle with x-axis rx and y-axis ry, you obtain such set of control points:
M1 (rx, 0); M2 (rx, (4/3)*ry*tg(f/4)); M3 (rx*(cos(f)+(4/3)*sin(f)*tg(f/4)), ry*(sin(f)- (4/3)*cos(f)*tg(f/4))); M4 (rx*cos(f), ry*(sin(f)); All coordinates here are absolute. Center of this ellipse is at (0, 0). I hope, you can shift and rotate it yourself? Here is only school math. Andrew M. ----- Original Message ----- From: Joe Gammad To: [email protected] Sent: Sunday, April 10, 2005 10:28 AM Subject: [svg-developers] Convert Ellipse to Cubic Bezier I have been struggling with this problem for some time and have not yet found an answer. Basically I want to convert a path containing an "elliptical arc curve" command to a "cubic bezier curve" command like so: Convert this: M (x y) A (rx ry rotation large-arc-flag sweep-flag x y) To this: M (x y) C (x1 y1 x2 y2 x y) This may seem like a backwards thing to do, but please just humor me. I don't want to get into the details as to why I want to carry this conversion out. I just do. Also I am sure there are parsers or conversion utility programs out there, however I would like to know how this can be done mathematically (i.e. with a paper and pencil and calculator). One wrinkle I see is that if the large-arc-flag is 1, then two or three cubic bezier commands (C) may be required to describe the path. There have been a number of questions in this forum regarding ellipses, so the solution to this problem may be of interest to other people as well. Any advice or help you can give me would be GREATLY appreciated. Thanks, Joe __________________________________ Do you Yahoo!? Yahoo! Small Business - Try our new resources site! http://smallbusiness.yahoo.com/resources/ ----- To unsubscribe send a message to: [EMAIL PROTECTED] -or- visit http://groups.yahoo.com/group/svg-developers and click "edit my membership" ---- ------------------------------------------------------------------------------ Yahoo! Groups Links a.. To visit your group on the web, go to: http://groups.yahoo.com/group/svg-developers/ b.. To unsubscribe from this group, send an email to: [EMAIL PROTECTED] c.. Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service. [Non-text portions of this message have been removed] ----- To unsubscribe send a message to: [EMAIL PROTECTED] -or- visit http://groups.yahoo.com/group/svg-developers and click "edit my membership" ---- Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/svg-developers/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
