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POProjection theory? (Implemented in GLSL)
 

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  1. POProjection theory? (Implemented in GLSL)
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    <p>OpenGL 3.x, because I don't want to be to far behind in tech.</p> <p>First of all, yes I know it's a lot. I am almost certain that the <code>vec3 transform(vec3)</code> function is fine, If nothing else I know that it does'nt contain the problem I'm coming here for.</p> <p>The bit of code I'm having problems with is (or should be) in the <code>vec3 project(vec3)</code> function. If I'm looking directly at, say, a box, it looks fine. If I turn the camera a bit so the box would be closer to a side of the screen (periferal vision), my happy box start's becoming a rectangle. While that is something I could live with for the game I'm putting it into, it's annoying.</p> <p>The basic theory behind the projection is: You have the point (x, y, z), you find the angles between that and the origin (where the camera is) and project it to a plane that is <code>nearz</code> distance out. Finding the angles is a matter of <code>angleX = atan(x/z)</code> and <code>angleY = atan(y/z)</code>. and using those two angles, you project them onto the near plane by doing <code>point = tan(angle) * nearz</code>. You then find the outer ridge of the screen by <code>edgeY = tan(fovy) * nearz</code> and <code>edgeX = tan(fovy * aspect) * nearz</code>. Finding the screen point using <code>screen = point/edge</code></p> <p>As a basic optimization I had, but removed in an attempt to fix this was to just take <code>screen = angle/fov</code></p> <p>Anything wrong with the theory of my projection function? Here's the implimentation:</p> <pre><code>#version 330 uniform vec3 model_location = vec3(0.0, 0.0, 0.0); uniform vec3 model_rotation = vec3(0.0, 0.0, 0.0); uniform vec3 model_scale = vec3(1.0, 1.0, 1.0); uniform vec3 camera_location = vec3(0.0, 0.0, 0.0); uniform vec3 camera_rotation = vec3(0.0, 0.0, 0.0); uniform vec3 camera_scale = vec3(1.0, 1.0, 1.0); uniform float fovy = 60.0; uniform float nearz = 0.01; uniform float farz = 1000.0; uniform float aspect = 1.0; vec3 transform(vec3 point) { vec3 translate = model_location - camera_location; vec3 rotate = radians(model_rotation); vec3 scale = model_scale / camera_scale; vec3 s = vec3(sin(rotate.x), sin(rotate.y), sin(rotate.z)); vec3 c = vec3(cos(rotate.x), cos(rotate.y), cos(rotate.z)); float sy_cz = s.y * c.z; float sy_sz = s.y * s.z; float cx_sz = c.x * s.z; vec3 result; result.x = ( point.x * ( ( c.y * c.z ) * scale.x ) ) + ( point.y * ( ( ( -cx_sz ) + ( s.x * sy_cz ) ) * scale.y ) ) + ( point.z * ( ( ( -s.x * s.z ) + ( c.x * sy_cz ) ) * scale.z ) ) + translate.x; result.y = ( point.x * ( ( c.y * s.z ) * scale.y ) ) + ( point.y * ( ( ( c.x * c.z ) + ( s.x * sy_sz ) ) * scale.y ) ) + ( point.z * ( ( ( -s.x * c.z ) + ( c.x * sy_sz ) ) * scale.z ) ) + translate.y; result.z = ( point.x * ( ( -s.y ) * scale.x ) ) + ( point.y * ( ( s.x * c.y ) * scale.y ) ) + ( point.z * ( ( c.x * c.y ) * scale.z ) ) + translate.z; return result; } vec4 project(vec3 point) { vec4 result = vec4(0.0); vec3 rotation = radians(camera_rotation); result.x = ( atan(point.x/point.z) - rotation.y ); result.y = ( atan(point.y/point.z) - rotation.x ); result.z = point.z/(farz - nearz); result.w = 1.0; result.x = tan(result.x) * nearz; result.y = tan(result.y) * nearz; vec2 bounds = vec2( tan(fovy * aspect) * nearz, tan(fovy) * nearz ); result.x = result.x / bounds.x; result.y = result.y / bounds.y; if (camera_rotation.z == 0) return result; float dist = sqrt( (result.x*result.x) + (result.y*result.y) ); float theta = atan(result.y/result.x) + rotation.z; result.x = sin(theta) * dist; result.y = cos(theta) * dist; return result; } layout(location = 0) in vec3 vertex_position; layout(location = 1) in vec2 texCoord; out vec2 uvCoord; void main() { uvCoord = texCoord; vec4 pos = project( transform(vertex_position) ); if (pos.z &lt; 0.0) return; gl_Position = pos; } </code></pre> <p>To answer a few anticipated questions:</p> <p>Q: Why not use GLM/some-other-mathimatics-lib?</p> <p>A:</p> <p>-I tryed a while ago. My "Hello world!" triangle was stuck in the center of the screen. using transformation matrics did'nt move it back forward, scale it, or anything.</p> <p>-Because learning how to figure thing's out for you're self is important. Doing this mean's that I learn how to tackle thing's like this, while still having something to fall back on if everything get's out-of-hand. (there's this fool's justification.)</p> <p>Q: Why not use matrics?</p> <p>A:</p> <p>-Those hate me too.</p> <p>-I'm doing it in a new way, If I used matrics then I would be doing it exactly how every tutorial say's to do it, instead of figuring it out for my-self.</p> <p>Tryed sources:</p> <p><a href="http://ogldev.atspace.co.uk/index.html" rel="nofollow noreferrer">http://ogldev.atspace.co.uk/index.html</a></p> <p><a href="http://www.swiftless.com/opengltuts/opengl4tuts.html" rel="nofollow noreferrer">http://www.swiftless.com/opengltuts/opengl4tuts.html</a></p> <p>Copyed letter for letter the GLSL shader's (vert &amp; frag) out of the "OpenGL Shading Language Third Edition", "Emulating the OpenGL Fixed Functionality" on pg. 288-293</p> <p>Tryed each multiple times, and tinkered with each to the point of insanity. Trying to program a war game, I got a wire-frame box to project into the peace symbol with one.</p> <p><strong>Edit:</strong></p> <p>The problem turned out to be the use of polar coord's as pointed out by datenwolf. A better equasion for the sake of projection using less advanced math was: <code>c = zNear * (p.x/p.y)</code> taken from the idea of the two triangles, the projected points triangle and the given points triangle, being preportional; and as a result using the same angle.</p> <p>assuming X and Y are given for the point that is to be projected, and their preportional triangles sidese are labeled A and C respectivly. You can take the equasion's <code>atan(Y/X) = angle</code> and <code>atan(C/A) = angle</code> and from that <code>atan(Y/X) = atan(C/A)</code> which then becomes <code>Y/X = C/A</code> and finishing with <code>C = A * (Y/X)</code> where A is the distance to the near plane. and C is the screen coord in the Y direction.</p>
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    1. USWolfgang Skyler
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    1. COJust some spelling nitpicking: The past form of try is tried.
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    2. COoop's, sorry. I'll keep that in mind. :)
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