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| -rw-r--r-- | ChangeLog | 5 | ||||
| -rw-r--r-- | examples/cairotwisted.c | 25 |
2 files changed, 26 insertions, 4 deletions
@@ -1,3 +1,8 @@ +2007-12-03 Behdad Esfahbod <behdad@gnome.org> + + * examples/cairotwisted.c: Add some more comments to document + the math involved. + 2007-11-30 Behdad Esfahbod <behdad@gnome.org> * examples/cairotwisted.c (two_points_distance), (curve_length), diff --git a/examples/cairotwisted.c b/examples/cairotwisted.c index 5697e57a..dfdf521a 100644 --- a/examples/cairotwisted.c +++ b/examples/cairotwisted.c @@ -291,10 +291,27 @@ typedef struct { } parametrized_path_t; -/* Project a point x,y onto a parameterized path. The final point is - * where you get if you walk on the path forward from the beginning for x - * units, then stop there and walk another y units perpendicular to the - * path at that point. */ +/* Project a point X,Y onto a parameterized path. The final point is + * where you get if you walk on the path forward from the beginning for X + * units, then stop there and walk another Y units perpendicular to the + * path at that point. In more detail: + * + * There's three pieces of math involved: + * + * - The parametric form of the Line equation + * http://en.wikipedia.org/wiki/Line + * + * - The parametric form of the Cubic Bézier curve equation + * http://en.wikipedia.org/wiki/B%C3%A9zier_curve + * + * - The Gradient (aka multi-dimensional derivative) of the above + * http://en.wikipedia.org/wiki/Gradient + * + * The parametric forms are used to answer the question of "where will I be + * if I walk a distance of X on this path". The Gradient is used to answer + * the question of "where will I be if then I stop, rotate left for 90 + * degrees and walk straight for a distance of Y". + */ static void point_on_path (parametrized_path_t *param, double *x, double *y) |