Curve Fitting: correct circular tangent length calculation

Method for scaling is still not perfect but quite close.
This commit is contained in:
Campbell Barton 2016-05-16 07:35:44 +10:00
parent bb7da630ba
commit a1a640f614
1 changed files with 47 additions and 7 deletions

View File

@ -429,14 +429,43 @@ static double points_calc_circumference_factor(
* (tangents that point away from each other).
* We could try support this but will likely cause extreme >1 scales which could cause other issues. */
// assert(angle >= len_tangent);
double factor = (angle / len_tangent) / (M_PI / 2);
factor = 1.0 - pow(1.0 - factor, 1.75);
assert(factor < 1.0 + DBL_EPSILON);
double factor = (angle / len_tangent);
assert(factor < (M_PI / 2) + DBL_EPSILON);
return factor;
}
else {
/* tangents are exactly aligned (think two opposite sides of a circle). */
return 1.0;
return (M_PI / 2);
}
}
/**
* Return the value which the distance between points will need to be scaled by,
* to define a handle, given both points are on a perfect circle.
*
* \note the return value will need to be multiplied by 1.3... for correct results.
*/
static double points_calc_circle_tangent_factor(
const double tan_l[],
const double tan_r[],
const uint dims)
{
const double angle_sin = len_vnvn(tan_l, tan_r, dims) / 2.0;
if (angle_sin != 0.0) {
const double tan_dot = dot_vnvn(tan_l, tan_r, dims);
double scale;
if (tan_dot > -1.0) {
const double angle = acos(tan_dot) / 2.0;
const double angle_cos = cos(angle);
scale = (1.0 - angle_cos) / (angle_sin * 2.0);
}
else {
scale = 1.0 / 2.0;
}
return (scale / angle_sin);
}
else {
return (1.0 / 3.0) * 0.75;
}
}
@ -451,9 +480,20 @@ static double points_calc_cubic_scale(
const double coords_length, uint dims)
{
const double len_direct = len_vnvn(v_l, v_r, dims);
const double len_circle_factor = points_calc_circumference_factor(tan_l, tan_r, dims) * 1.75;
const double len_points = min(coords_length, len_circle_factor * len_direct);
return (len_direct + ((len_points - len_direct) * len_circle_factor)) / 3.0;
const double len_circle_factor = points_calc_circle_tangent_factor(tan_l, tan_r, dims);
/* if this curve is a circle, this value doesn't need modification */
const double len_circle_handle = (len_direct * (len_circle_factor / 0.75));
/* scale by the difference from the circumference distance */
const double len_circle = len_direct * points_calc_circumference_factor(tan_l, tan_r, dims);
double scale_handle = (coords_length / len_circle);
/* Could investigate an accurate calculation here,
* though this gives close results */
scale_handle = ((scale_handle - 1.0) * 1.75) + 1.0;
return len_circle_handle * scale_handle;
}
static void cubic_from_points_fallback(