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Simplify rectircle equations by using trigonometric super-ellipse parametrization

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Kovid Goyal
2025-05-10 07:31:33 +05:30
parent a597764245
commit 20e5c7b004
1 changed files with 19 additions and 36 deletions
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55
kitty/decorations.c
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@@ -1226,39 +1226,20 @@ fading_vline(Canvas *self, uint level, uint num, Edge fade) {
typedef struct Rectircle Rectircle; typedef struct Rectircle Rectircle;
typedef struct Rectircle { typedef struct Rectircle {
uint a, b; double a, b, yexp, xexp, x_sign, y_sign, x_start, y_start;
double yexp, xexp, adjust_x;
uint cell_width;
curve_func x, y; curve_func x, y;
} Rectircle; } Rectircle;
static double static double
rectircle_lower_half_y(void *v, double t) { rectircle_x(void *v, double t) {
Rectircle *r = v; Rectircle *r = v;
return r->b * t; // 0 -> top of cell, 1 -> middle of cell return r->x_start + r->x_sign * r->a * pow(cos(t * (M_PI / 2.0)), r->xexp);
} }
static double static double
rectircle_upper_half_y(void *v, double t) { rectircle_y(void *v, double t) {
Rectircle *r = v; Rectircle *r = v;
return r->b * (2. - t); // 0 -> bottom of cell, 1 -> middle of cell return r->y_start + r->y_sign * r->b * pow(sin(t * (M_PI / 2.0)), r->yexp);
}
// x(t). To get this we first need |y(t)|/b. This is just t since as t goes
// from 0 to 1 y goes from either 0 to b or 0 to -b
static double
rectircle_left_half_x(void *v, double t) {
Rectircle *r = v;
double xterm = 1 - pow(t, r->yexp);
return floor(r->cell_width - fabs(r->a * pow(xterm, r->xexp)) - r->adjust_x);
}
static double
rectircle_right_half_x(void *v, double t) {
Rectircle *r = v;
double xterm = 1 - pow(t, r->yexp);
return ceil(fabs(r->a * pow(xterm, r->xexp)));
} }
static Rectircle static Rectircle
@@ -1267,10 +1248,14 @@ rectcircle(Canvas *self, Corner which) {
Return two functions, x(t) and y(t) that map the parameter t which must be Return two functions, x(t) and y(t) that map the parameter t which must be
in the range [0, 1] to x and y coordinates in the cell. The rectircle equation in the range [0, 1] to x and y coordinates in the cell. The rectircle equation
we use is: we use is:
(|x| / a) ^ (2a / r) + (|y| / b) ^ (2b / r) = 1 (|x| / a) ^ (2a / r) + (|y| / b) ^ (2b / r) = 1
where 2a = width, 2b = height and r is radius where 2a = width, 2b = height and r is radius
See https://math.stackexchange.com/questions/1649714
This is a super-ellipse, its parametrized form is:
x = ± a * (cos(theta) ^ (r / a)); y = ± b * (sin(theta) ^ (r / b)); theta is in [0, pi/2]
https://en.wikipedia.org/wiki/Superellipse
The plus minus signs are chosen to give the four quadrants.
The entire rectircle fits in four cells, each cell being one quadrant The entire rectircle fits in four cells, each cell being one quadrant
of the full rectircle and the origin being the center of the rectircle. of the full rectircle and the origin being the center of the rectircle.
@@ -1278,18 +1263,16 @@ rectcircle(Canvas *self, Corner which) {
╭╮ ╭─╮ ╭╮ ╭─╮
╰╯ │ │ ╰╯ │ │
╰─╯ ╰─╯
See https://math.stackexchange.com/questions/1649714
*/ */
double radius = self->width / 2.; double radius = self->width / 2., a = self->width / 2., b = self->height / 2.;
uint cell_width_is_odd = (self->width / self->supersample_factor) & 1;
Rectircle ans = { Rectircle ans = {
.a = half_width(self), .b = half_height(self), .a = a, .b = b,
.yexp = self->height / radius, .xexp = radius / a, .yexp = radius / b,
.xexp = radius / self->width, .x_sign = which & RIGHT_EDGE ? 1. : -1,
.cell_width = self->width, .x_start = which & RIGHT_EDGE ? 0. : 2 * a,
.adjust_x = cell_width_is_odd * self->supersample_factor, .y_start = which & BOTTOM_EDGE ? 0. : 2 * b,
.x = which & LEFT_EDGE ? rectircle_left_half_x : rectircle_right_half_x, .y_sign = which & BOTTOM_EDGE ? 1. : -1,
.y = which & TOP_EDGE ? rectircle_upper_half_y : rectircle_lower_half_y, .x = rectircle_x, .y = rectircle_y,
}; };
return ans; return ans;