diff options
| -rw-r--r-- | src/fl_arc.cxx | 62 |
1 files changed, 31 insertions, 31 deletions
diff --git a/src/fl_arc.cxx b/src/fl_arc.cxx index 27bdaf4f4..a4895f68e 100644 --- a/src/fl_arc.cxx +++ b/src/fl_arc.cxx @@ -1,5 +1,5 @@ // -// "$Id: fl_arc.cxx,v 1.4.2.3.2.4 2002/05/03 12:49:36 easysw Exp $" +// "$Id: fl_arc.cxx,v 1.4.2.3.2.5 2002/05/03 19:33:39 easysw Exp $" // // Arc functions for the Fast Light Tool Kit (FLTK). // @@ -33,38 +33,38 @@ void fl_arc(double x, double y, double r, double start, double end) { // draw start point accurately: - double A = start*(M_PI/180); - double X = r*cos(A); - double Y = -r*sin(A); - fl_vertex(x+X,y+Y); + + double A = start*(M_PI/180); // Initial angle (radians) + double X = r*cos(A); // Initial displacement, (X,Y) + double Y = -r*sin(A); // from center to initial point + fl_vertex(x+X,y+Y); // Insert initial point - // number of segments per radian: - int n; { - double x1 = fl_transform_dx(r,0); - double y1 = fl_transform_dy(r,0); - double r1 = x1*x1+y1*y1; - x1 = fl_transform_dx(0,r); - y1 = fl_transform_dy(0,r); - double r2 = x1*x1+y1*y1; - if (r2 < r1) r1 = r2; - n = int(sqrt(r1)*.841471); - if (n < 2) n = 2; - if (n > 60) n = 60; + // Maximum arc length to approximate with chord with error <= 0.125 + + double epsilon; { + double r1 = hypot(fl_transform_dx(r,0), // Horizontal "radius" + fl_transform_dy(r,0)); + double r2 = hypot(fl_transform_dx(0,r), // Vertical "radius" + fl_transform_dy(0,r)); + + if (r2 < r1) r1 = r2; // r1 = minimum "radius" + r2 = 1.0 - 0.125/r1; // r2 = cos(epsilon/2) + if (r2 < 0.5) r2 = 0.5; // minimum 3 chords/circle + epsilon = 2*acos(r2); // Maximum arc angle } - double epsilon = 1.0/n; - double E = end*(M_PI/180); - int i = int((E-A)*n); - if (i < 0) {i = -i; epsilon = -epsilon;} - double epsilon2 = epsilon/2; - for (; i>1; i--) { - X += epsilon*Y; - Y -= epsilon2*X; - fl_vertex(x+X,y+Y); - Y -= epsilon2*X; + A = end*(M_PI/180) - A; // Displacement angle (radians) + int i = int(ceil(fabs(A)/epsilon)); // Segments in approximation + + if (i) { + epsilon = A/i; // Arc length for equal-size steps + double cos_e = cos(epsilon);// Rotation coefficients + double sin_e = sin(epsilon); + do { + double Xnew = cos_e*X + sin_e*Y; + Y = -sin_e*X + cos_e*Y; + fl_vertex(x + (X=Xnew), y + Y); + } while (--i); } - - // draw the end point accurately: - fl_vertex(x+r*cos(E), y-r*sin(E)); } #if 0 // portable version. X-specific one in fl_vertex.cxx @@ -74,5 +74,5 @@ void fl_circle(double x,double y,double r) { #endif // -// End of "$Id: fl_arc.cxx,v 1.4.2.3.2.4 2002/05/03 12:49:36 easysw Exp $". +// End of "$Id: fl_arc.cxx,v 1.4.2.3.2.5 2002/05/03 19:33:39 easysw Exp $". // |