GLSL Parametric Curve Plotter

Question

I am trying to implement a parametric curve plotter on a fragment shader in GLSL.

I managed to make a rudimentary one by iterating the parameter and drawing a circle for each computed position.

You can find the (working and commented) code here.

Here are my questions:

• I would like to plot it with a line. From what I have understood, I see two different ways I could do it :

  1. by computing the distance between each pixel and the computed position inside the loop, accumulate the computed value in a float variable, and then draw the curve using a step function.

     I tried doing this and it seems like I only compute the distance for the one t position:

     #define PI 3.14
     
     void mainImage( out vec4 fragColor, in vec2 fragCoord )
     {
         vec2 uv = -1. + 2.*fragCoord.xy / iResolution.xy;
         uv.x *= iResolution.x/iResolution.y;
         vec3 color = vec3(0.);
         vec2 pos;
         float dist;
     
         for(float t=-2.; t<2.02; t+=.02){
     
             pos.x = sin(4.*t+(iGlobalTime));
             pos.y = cos(6.*t);
     
             dist += 1.-sqrt(pow((uv.x-pos.x),2.)+pow((uv.y-pos.y),2.));
     
             color += vec3(dist);
     
     
         }//for
     
         fragColor = mix(vec4(0.0), vec4(1.0), dist);
     
     }
     

  2. By drawing line segment between each consecutive positions of the parameter

     I found this implementation that seems to do what I am trying to achieve, but i don't quite understand why they are using the previous position of the parameter.

• Is there a way to do such a function without a for loop managing the parameter?

Last precision : I'm only suing a fragment shader because my goal is to upload it on a VJing software that manages fragment shaders