Implement antialiasing logic for line segments and triangles in GLSL shaders - three.js

Question

I'm building 2D Graph structure based on Three.js, all elements of the graph (nodes, edges, triangles for arrows) calculated in shaders. I was able to reach a good level of antialiasing for nodes (circles) but stuck with same task for lines and triangles.
I was able to reach a good antialiasing results for nodes (circles) with and without stroke following this question: How can I add a uniform width outline to WebGL shader drawn circles/ellipses (drawn using edge/distance antialiasing) , my code, responsible for antialiasing alpha:
`float strokeWidth = 0.09;
float outerEdgeCenter = 0.5 - strokeWidth;
float d = distance(vUV, vec2(.5, .5));
float delta = fwidth(d);
float alpha = 1.0 - smoothstep(0.45 - delta, 0.45, d);
float stroke = 1.0 - smoothstep(outerEdgeCenter - delta,
outerEdgeCenter + delta, d);`
But now I'm completely stack with edges and triangles to do same stuff.
Here is an example of shapes images that I have now (on non retina displays):
To reduce under-sampling artifacts I want to do similar algorithms (as for circles) directly in shaders by manipulating alpha and already find some materials related to this topic:
https://thebookofshaders.com/glossary/?search=smoothstep - seems to be the closest solution but unfortunately I wasn't able to implement it properly and figure out how to set up y equation for segmented lines.
https://discourse.threejs.org/t/shader-to-create-an-offset-inward-growing-stroke/6060/12 - last answer, looks promising but not give me proper result.
https://www.shadertoy.com/view/4dcfW8 - also do not give proper result.
Here is an examples of my shaders for lines and triangles:
Line VertexShader (is a slightly adapted version of WestLangley's LineMaterial shader):
`precision highp float;
#include <common>
#include <color_pars_vertex>
#include <fog_pars_vertex>
#include <logdepthbuf_pars_vertex>
#include <clipping_planes_pars_vertex>
uniform float linewidth;
uniform vec2 resolution;
attribute vec3 instanceStart;
attribute vec3 instanceEnd;
attribute vec3 instanceColorStart;
attribute vec3 instanceColorEnd;
attribute float alphaStart;
attribute float alphaEnd;
attribute float widthStart;
attribute float widthEnd;
varying vec2 vUv;
varying float alphaTest;
void trimSegment( const in vec4 start, inout vec4 end ) {
// trim end segment so it terminates between the camera plane and the near plane
// conservative estimate of the near plane
float a = projectionMatrix[ 2 ][ 2 ]; // 3nd entry in 3th column
float b = projectionMatrix[ 3 ][ 2 ]; // 3nd entry in 4th column
float nearEstimate = - 0.5 * b / a;
float alpha = ( nearEstimate - start.z ) / ( end.z - start.z );
end.xyz = mix( start.xyz, end.xyz, alpha );
}
void main() {
#ifdef USE_COLOR
vColor.xyz = ( position.y < 0.5 ) ? instanceColorStart : instanceColorEnd;
alphaTest = ( position.y < 0.5 ) ? alphaStart : alphaEnd;
#endif
float aspect = resolution.x / resolution.y;
vUv = uv;
// camera space
vec4 start = modelViewMatrix * vec4( instanceStart, 1.0 );
vec4 end = modelViewMatrix * vec4( instanceEnd, 1.0 );
// special case for perspective projection, and segments that terminate either in, or behind, the camera plane
// clearly the gpu firmware has a way of addressing this issue when projecting into ndc space
// but we need to perform ndc-space calculations in the shader, so we must address this issue directly
// perhaps there is a more elegant solution -- WestLangley
bool perspective = ( projectionMatrix[ 2 ][ 3 ] == - 1.0 ); // 4th entry in the 3rd column
if (perspective) {
if (start.z < 0.0 && end.z >= 0.0) {
trimSegment( start, end );
} else if (end.z < 0.0 && start.z >= 0.0) {
trimSegment( end, start );
}
}
// clip space
vec4 clipStart = projectionMatrix * start;
vec4 clipEnd = projectionMatrix * end;
// ndc space
vec2 ndcStart = clipStart.xy / clipStart.w;
vec2 ndcEnd = clipEnd.xy / clipEnd.w;
// direction
vec2 dir = ndcEnd - ndcStart;
// account for clip-space aspect ratio
dir.x *= aspect;
dir = normalize( dir );
// perpendicular to dir
vec2 offset = vec2( dir.y, - dir.x );
// undo aspect ratio adjustment
dir.x /= aspect;
offset.x /= aspect;
// sign flip
if ( position.x < 0.0 ) offset *= - 1.0;
// endcaps, to round line corners
if ( position.y < 0.0 ) {
// offset += - dir;
} else if ( position.y > 1.0 ) {
// offset += dir;
}
// adjust for linewidth
offset *= (linewidth * widthStart);
// adjust for clip-space to screen-space conversion // maybe resolution should be based on viewport ...
offset /= resolution.y;
// select end
vec4 clip = ( position.y < 0.5 ) ? clipStart : clipEnd;
// back to clip space
offset *= clip.w;
clip.xy += offset;
gl_Position = clip;
vec4 mvPosition = ( position.y < 0.5 ) ? start : end; // this is an approximation
#include <logdepthbuf_vertex>
#include <clipping_planes_vertex>
#include <fog_vertex>
}`
Line FragmentShader:
`precision highp float;
#include <common>
#include <color_pars_fragment>
#include <fog_pars_fragment>
#include <logdepthbuf_pars_fragment>
#include <clipping_planes_pars_fragment>
uniform vec3 diffuse;
uniform float opacity;
varying vec2 vUv;
varying float alphaTest;
void main() {
if ( abs( vUv.y ) > 1.0 ) {
float a = vUv.x;
float b = ( vUv.y > 0.0 ) ? vUv.y - 1.0 : vUv.y + 1.0;
float len2 = a * a + b * b;
if ( len2 > 1.0 ) discard;
}
vec4 diffuseColor = vec4( diffuse, alphaTest );
#include <logdepthbuf_fragment>
#include <color_fragment>
gl_FragColor = vec4( diffuseColor.rgb, diffuseColor.a );
#include <premultiplied_alpha_fragment>
#include <tonemapping_fragment>
#include <encodings_fragment>
#include <fog_fragment>
}`
Triangle vertex shader:
`precision highp float;
uniform mat4 modelViewMatrix;
uniform mat4 projectionMatrix;
uniform float zoomLevel;
attribute vec3 position;
attribute vec3 vertexPos;
attribute vec3 color;
attribute float alpha;
attribute float xAngle;
attribute float yAngle;
attribute float xScale;
attribute float yScale;
varying vec4 vColor;
// transforms the 'positions' geometry with instance attributes
vec3 transform( inout vec3 position, vec3 T) {
position.x *= xScale;
position.y *= yScale;
// Rotate the position
vec3 rotatedPosition = vec3(
position.x * yAngle + position.y * xAngle,
position.y * yAngle - position.x * xAngle, 0);
position = rotatedPosition + T;
// return the transformed position
return position;
}
void main() {
vec3 pos = position;
vColor = vec4(color, alpha);
// transform it
transform(pos, vertexPos);
gl_Position = projectionMatrix * modelViewMatrix * vec4( pos, 1.0 );
}`
Triangle FragmentShader:
`precision highp float;
varying vec4 vColor;
void main() {
gl_FragColor = vColor;
}`
Will really appreciate any help on how to do it or suggestion of right direction for further investigations. Thank you!