I think you really should look at shaders for this sort of thing. It will be a lot simpler since each rendered fragment comes with a screen coordinate in glFragCoord. You can then interpolate the colour of the fragment from any set of coordinates/colours supplied in uniforms with any function you like.

Circularinterpolationprogram example

I also think you will have to do this by yourself without help of the GL API, so either in a shader or on the CPU: software resterization of the circle to find the startingpoint of the lines, line-line intersection to find the other point, calculatind the interpolated color as the color for the endpoint and then you can draw the lines (with massive overdraw) via GL.

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glBegin(GL_TRIANGLES); glColor3f(1.0, 0.0, 0.0); glVertex3f( 0.0f, 1.0f, 0.0f); glColor3f(0.0, 1.0, 0.0); glVertex3f(-1.0f,-1.0f, 0.0f); glColor3f(0.0, 0.0, 1.0); glVertex3f( 1.0f,-1.0f, 0.0f); glEnd();

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Circularinterpolationprogram example PDF

When I draw a filled circle using the code below it just draws a yellow circle and does not interpolate anything. Is there a keyword GL_?? that I can use for interpolation?

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With this logic I think I will be able to create the figure I want because from the circle boundary to triangle boundary, the lines I will draw will be interpolated.

You can now use maths to find the intersection point of the pixel-centre and vertex-vertex line segments (all on cpu). This gives a coordinate to read the colour from the rendered texture.

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To Be more clear, at the lower left corner of the circle I have a blue value. And inside of the circle is colorless until I meet the lower left corner of the triangle which is red. From that blue to red there needs to be an interpolation. This process needs to be done for every pixel of the circle.

In the second picture. What I am trying to accomplish adding a circle outside of that triangle and create a natural smooth looking picture.

Let’s say I have a triangle. Each vertex of that triangle has a color value, inside of that triangle the colors were interpolated. a well known example:

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Thanks for all the comments to finish this initial task. However I am open to new comments to have a better looking, smoother result and how I can achieve that.

As you are drawing just a line loop, OpenGL does not generate fragments for the space between the circle and the triangle so it has to stay black. Try drawing a filled circle (maybe as a triangle fan) and see if the interpolation between the outer vertices and the center matches your taste. As the interpolation will always be linear, you might have to tessellate your mesh to get a different appearance. You can also do more complicated fragment accurate interpolation with a fragment shader…

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However my problem is about 3a and 3b now, how can I find the intersection of a line to a plane (triangular or polygonal) and can I have the color of that point on the screen?

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In the third picture I am showing how I have drawn the circles using the outer triangle vertices. For each portion of the circle I make a loop (i.e. from PI/2 to PI) and for ever pixel on the circle boundary I use the corresponding triangle’s out 2 vertices and draw a triangle between those three points

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I wanna a draw a circle or ellipse outside of this triangle and paint the unpainted portion of this ellipse by interpolating the colors of the triangle. What I mean is FROM the borders of the circle TO the borders of triangle there needs to be an interpolation logic. We can assume the borders of the ellipse has a color value equal to the blue.

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The first picture is the original pentagon. I draw that using 9 triangles composed by 8 vertices. Each vertex has a color power value from blue to red.