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/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
// Preprocess the radii for computing the distance approximation. This should
// be used in the vertex shader if possible to avoid doing expensive division
// in the fragment shader. When dealing with a point (zero radii), approximate
// it as an ellipse with very small radii so that we don't need to branch.
vec2 inverse_radii_squared(vec2 radii) {
return 1.0 / max(radii * radii, 1.0e-6);
}
#ifdef WR_FRAGMENT_SHADER
// One iteration of Newton's method on the 2D equation of an ellipse:
//
// E(x, y) = x^2/a^2 + y^2/b^2 - 1
//
// The Jacobian of this equation is:
//
// J(E(x, y)) = [ 2*x/a^2 2*y/b^2 ]
//
// We approximate the distance with:
//
// E(x, y) / ||J(E(x, y))||
//
// See G. Taubin, "Distance Approximations for Rasterizing Implicit
// Curves", section 3.
//
// A scale relative to the unit scale of the ellipse may be passed in to cause
// the math to degenerate to length(p) when scale is 0, or otherwise give the
// normal distance approximation if scale is 1.
float distance_to_ellipse_approx(vec2 p, vec2 inv_radii_sq, float scale) {
vec2 p_r = p * inv_radii_sq;
float g = dot(p, p_r) - scale;
vec2 dG = (1.0 + scale) * p_r;
return g * inversesqrt(dot(dG, dG));
}
// Slower but more accurate version that uses the exact distance when dealing
// with a 0-radius point distance and otherwise uses the faster approximation
// when dealing with non-zero radii.
float distance_to_ellipse(vec2 p, vec2 radii) {
return distance_to_ellipse_approx(p, inverse_radii_squared(radii),
float(all(greaterThan(radii, vec2(0.0)))));
}
float distance_to_rounded_rect(
vec2 pos,
vec3 plane_tl,
vec4 center_radius_tl,
vec3 plane_tr,
vec4 center_radius_tr,
vec3 plane_br,
vec4 center_radius_br,
vec3 plane_bl,
vec4 center_radius_bl,
vec4 rect_bounds
) {
// Clip against each ellipse. If the fragment is in a corner, one of the
// branches below will select it as the corner to calculate the distance
// to. We use half-space planes to detect which corner's ellipse the
// fragment is inside, where the plane is defined by a normal and offset.
// If outside any ellipse, default to a small offset so a negative distance
// is returned for it.
vec4 corner = vec4(vec2(1.0e-6), vec2(1.0));
// Calculate the ellipse parameters for each corner.
center_radius_tl.xy = center_radius_tl.xy - pos;
center_radius_tr.xy = (center_radius_tr.xy - pos) * vec2(-1.0, 1.0);
center_radius_br.xy = pos - center_radius_br.xy;
center_radius_bl.xy = (center_radius_bl.xy - pos) * vec2(1.0, -1.0);
// Evaluate each half-space plane in turn to select a corner.
if (dot(pos, plane_tl.xy) > plane_tl.z) {
corner = center_radius_tl;
}
if (dot(pos, plane_tr.xy) > plane_tr.z) {
corner = center_radius_tr;
}
if (dot(pos, plane_br.xy) > plane_br.z) {
corner = center_radius_br;
}
if (dot(pos, plane_bl.xy) > plane_bl.z) {
corner = center_radius_bl;
}
// Calculate the distance of the selected corner and the rectangle bounds,
// whichever is greater.
return max(distance_to_ellipse_approx(corner.xy, corner.zw, 1.0),
signed_distance_rect(pos, rect_bounds.xy, rect_bounds.zw));
}
#endif
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