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occurred Jun 22, 2014 at 22:47

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edited Jun 22, 2014 at 21:06

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*Update: Let me clarify what's going on with this picture:

Now, in contrast to that, I am later interested in knowing if the single vertex v0 is visible (I don't have any information about triangles at that point). So I project the vertex v0 which will land at (1.1, 1.1) in screen space and end up with a z-value as well. However this z-value will be different than the one that is in the z-buffer for this pixel, because the z-value in the z-buffer has been calculated using the barycentric weights of the triangle for the middle point of the triangle. So I can't determine if the vertex v0 is visible or not.

To rephrase: The z-value in the z-buffer is from the red dot in the image (produced when rendering the triangle), and it is different from the z-value of the projection of the vertex v0 which is exactly at position v0.

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edited Jun 22, 2014 at 14:30

Ela782

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*Update: Let me clarify what's going on with this picture:

Triangle

Let's say v0 = (1.1, 1.1), v1 = (6.7, 2.1), v2 = (3.7, 6.7) after projection to screen-space. When rendering/rasterizing the triangle, I have a loop

for x = 1 to 7 // from floor(min(v0.x, v1.x, v2.x)) to ceil(max(v0.x, v1.x, v2.x))
    for y = 1 to 7 // same for y
        current_pixel_center = (x+0.5, y+0.5); // we want calculations to use the center of pixels
        alpha = ..., beta = ..., gamma = ...; // calculate the barycentric weights for current_pixel_center
        if all 3 bary. weights > 0 // means the pixel is inside the triangle
            z_value_of_curr_pixel = alpha * v0.z + beta * v1.z + gamma * v2.z;
            // Do the z-test and then draw the pixel at position (x, y), and set the z-buffer at (x, y) to the new value 'z_value_of_curr_pixel'

So the pixel at position (1, 1) in my drawing gets some color and z-value based on the barycentric weights calculated for this point, it is close to v0 so probably something like alpha = 0.95, beta = 0.02, gamma = 0.03.

Now, in contrast to that, I am later interested in knowing if the single vertex v0 is visible (I don't have any information about triangles at that point). So I project the vertex v0 which will land at (1.1, 1.1) in screen space and end up with a z-value as well. However this z-value will be different than the one that is in the z-buffer for this pixel, because the z-value in the z-buffer has been calculated using the barycentric weights of the triangle for the middle point of the triangle. So I can't determine if the vertex v0 is visible or not.

*Update: Let me clarify what's going on with this picture:

Triangle

Let's say v0 = (1.1, 1.1), v1 = (6.7, 2.1), v2 = (3.7, 6.7) after projection to screen-space. When rendering/rasterizing the triangle, I have a loop

for x = 1 to 7 // from floor(min(v0.x, v1.x, v2.x)) to ceil(max(v0.x, v1.x, v2.x))
    for y = 1 to 7 // same for y
        current_pixel_center = (x+0.5, y+0.5); // we want calculations to use the center of pixels
        alpha = ..., beta = ..., gamma = ...; // calculate the barycentric weights for current_pixel_center
        if all 3 bary. weights > 0 // means the pixel is inside the triangle
            z_value_of_curr_pixel = alpha * v0.z + beta * v1.z + gamma * v2.z;
            // Do the z-test and then draw the pixel at position (x, y), and set the z-buffer at (x, y) to the new value 'z_value_of_curr_pixel'

So the pixel at position (1, 1) in my drawing gets some color and z-value based on the barycentric weights calculated for this point, it is close to v0 so probably something like alpha = 0.95, beta = 0.02, gamma = 0.03.

Now, in contrast to that, I am later interested in knowing if the single vertex v0 is visible (I don't have any information about triangles at that point). So I project the vertex v0 which will land at (1.1, 1.1) in screen space and end up with a z-value as well. However this z-value will be different than the one that is in the z-buffer for this pixel, because the z-value in the z-buffer has been calculated using the barycentric weights of the triangle for the middle point of the triangle. So I can't determine if the vertex v0 is visible or not.

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asked Jun 22, 2014 at 10:56

Ela782

131
4

How to determine the visibility of a single vertex, given a viewpoint?

I have a 3D triangle mesh, and I want to know, given a viewpoint (defined by a model, view and projection matrix), if a certain vertex is visible or not.

My approach was to render the mesh using standard software rasterization (I can't use OpenGL/DX), i.e. project all the triangle vertices to screen-space, then loop through each triangle's bounding-box and rasterize/shade the pixels inside the triangle (using barycentric coordinates). I'm also using a z-Buffer here, and the rendering works fine.

To find out if a certain vertex point is visible, my naive idea was then to just project that vertex from 3D to 2D using the same matrices, and comparing the z-value I get for that pixel to the value in the z-Buffer.

However, this approach does not work, I get vertices flagged as visible that should be invisible and vice versa.

I believe this is because of the following: When I render the triangles, I loop over the bounding-box of the triangle and set the color and depth value by interpolating a value between the 3 triangle vertices, using barycentric coordinates. Thus, the depth value written to the z-buffer for a given point (x, y) on screen is a linear combination of the z-value of the 3 vertices that make up the triangle. In contrast to that, when I project the single vertex later, I render the exact point, independent from any triangles, and thus get a different z-value for the same (x, y) location on screen.

Is my assumption on why it is not working correct, and how would I correctly determine the visibility of a vertex in the mesh?

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How to determine the visibility of a single vertex, given a viewpoint?