Hi Bill - thanks for the reply. You're right - perhaps I can derive the math from that fact. My B-Spline code implements the "openness" via the knot vector, but I believe you can achieve the same result by using a periodic spline that repeats the control points instead. I'll give it a shot. <div class="gmail_quote">On Mon, Apr 6, 2009 at 11:30 PM, Bill Spitzak <<a href="mailto:spitzak@thefoundry.co.uk">spitzak@thefoundry.co.uk</a>> wrote: <blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> Aren't the end points as though there are 2 b-spline control points at that location? Ie pretend there is one more point before and after the ends of your curve but equal to those points, then do your algorithm. Gerald Hansford wrote: <blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"><div><div></div><div class="h5"> Hi - thanks as always to the tremendous team responsible for Cairo - it's an excellent library. Does anyone have any experience rendering open, cubic uniform B-Splines using Cairo? I know that it does not have explicit support for B-Splines, but my understanding is that one can derive the series of Bézier splines represented implicity in a B-Spline. In fact I have code that does this for the open & periodic cases for quadratic b-splines, as well as the periodic case for cubic B-Splines. For that, my code looks about like this: Vec2f q0, q1, q2, q3; q0 = ( spline.getControlPoint( 0 ) + spline.getControlPoint( 1 ) * 4.0f + spline.getControlPoint( 2 ) ) / 6.0f; moveTo( q0 ); int lastPt = ( spline.isLoop() ) ? numPoints : numPoints - 3; for( int i = 0; i < lastPt; ++i ) { Vec2f p1 = spline.getControlPoint( ( i + 1 ) % numPoints ); Vec2f p2 = spline.getControlPoint( ( i + 2 ) % numPoints ); Vec2f p3 = spline.getControlPoint( ( i + 3 ) % numPoints ); q1 = p1 * ( 4.0f / 6.0f ) + p2 * ( 2.0f / 6.0f ); q2 = p1 * ( 2.0f / 6.0f ) + p2 * ( 4.0f / 6.0f ); q3 = p1 * ( 1.0f / 6.0f ) + p2 * ( 4.0f / 6.0f ) + p3 * ( 1.0f / 6.0f ); curveTo( q1, q2, q3 ); } The trouble comes when I try to address the open cubic case (where the curve passes through the endpoints of the b-spline). All of the literature on the topic which I can actually understand seems to be about the periodic case. I know that in the open case, a b-spline with 4 control points exactly maps to the bezier curve with the same control points. Also through experimentation I can tell that the non-end segments of an open b-spline with >= 6 points correspond to the periodic case. However I am still at a loss as to how one would glue all of this information together, and I haven't managed to get deep enough in the relevant math to follow discussions of how knot insertion or blossoming helps me solve this problem. Any help from someone experienced in all of this would be *very* much appreciated. Thanks in advance... </div></div> ------------------------------------------------------------------------ _______________________________________________ cairo mailing list <a href="mailto:cairo@cairographics.org" target="_blank">cairo@cairographics.org</a> <a href="http://lists.cairographics.org/mailman/listinfo/cairo" target="_blank">http://lists.cairographics.org/mailman/listinfo/cairo</a> </blockquote> -- Bill Spitzak, Senior Software Engineer The Foundry, 618 Hampton Drive, Venice, CA, 90291, USA Tel: +1 310 399-4555 * Fax: +1 310 450-4516 * Web: <a href="http://www.thefoundry.co.uk" target="_blank">www.thefoundry.co.uk</a> The Foundry Visionmongers Ltd * Registered in England and Wales No: 4642027 </blockquote></div>