85 lines
2.5 KiB
Plaintext
85 lines
2.5 KiB
Plaintext
#version 150 compatibility
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out EllipsoidData {
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vec2 q_tilde;
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float inv_e;
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vec3 nml_e_eye;
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vec3 nml_v_eye;
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vec2 zw_e_clip;
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vec2 zw_v_clip;
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vec3 v_eye;
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} Vout;
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void generate_vertex(in vec3 center, in mat3 T, in mat3 inv_T, in vec2 t, in vec3 m_tilde, in vec3 x_tilde, in vec3 y_tilde, in vec3 e_tilde)
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{
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// set q coordinates of corner
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Vout.q_tilde = t;
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// compute the corner point in homogeneous object coordinates
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vec3 V_tilde = m_tilde + t.x*x_tilde + t.y*y_tilde;
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vec4 V = vec4(T*V_tilde + center, 1.0);
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// compute vector from eye to vertex in eye space
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Vout.v_eye = (gl_ModelViewMatrix*V).xyz;
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// compute components to compute normal in eye space
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Vout.nml_v_eye = gl_NormalMatrix*(inv_T*(V_tilde - e_tilde));
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gl_Position = gl_ModelViewProjectionMatrix * V;
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Vout.zw_v_clip = gl_Position.zw - Vout.zw_e_clip;
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EmitVertex();
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}
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void cover_ellipsoid_with_quad(in vec3 center, in vec3 enc_T0, in vec3 enc_T1)
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{
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// decompress the matrix T
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mat3 T;
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T[0] = enc_T0;
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T[1].x = enc_T0.y;
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T[1].yz = enc_T1.xy;
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T[2].x = enc_T0.z;
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T[2].yz = enc_T1.yz;
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// invert the matrix T
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mat3 inv_T;
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float inv_denom = 1.0 / dot(T[0], cross(T[1], T[2]));
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inv_T[0] = inv_denom*cross(T[1], T[2]);
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inv_T[1] = inv_denom*cross(T[2], T[0]);
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inv_T[2] = inv_denom*cross(T[0], T[1]);
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// determine eye point in parameter space
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vec3 e = gl_ModelViewMatrixInverse[3].xyz;
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vec3 e_tilde = inv_T*(e - center);
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// compute helper
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float inv_e_square = 1.0 / dot(e_tilde, e_tilde);
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// determine silhoutte center in parameter space
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vec3 m_tilde = inv_e_square*e_tilde;
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// determine radius of silhouette in parameter space
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float r = sqrt(1.0 - inv_e_square);
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// compute vector x of length r orthogonal to e in parameter space
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vec3 x_tilde = vec3(0, 0, 0);
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if (abs(e_tilde[1]) > abs(e_tilde[0]))
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x_tilde[0] = 1.0;
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else
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x_tilde[1] = 1.0;
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x_tilde = r*normalize(cross(x_tilde, e_tilde));
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// compute vector y of length r orthogonal to x and e in parameter space
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vec3 y_tilde = r*normalize(cross(e_tilde, x_tilde));
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Vout.inv_e = sqrt(inv_e_square);
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Vout.zw_e_clip = (gl_ModelViewProjectionMatrix * gl_ModelViewMatrixInverse[3]).zw;
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Vout.nml_e_eye = gl_NormalMatrix*(inv_T*e_tilde);
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generate_vertex(center, T, inv_T, vec2(-1.0, -1.0), m_tilde, x_tilde, y_tilde, e_tilde);
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generate_vertex(center, T, inv_T, vec2( 1.0, -1.0), m_tilde, x_tilde, y_tilde, e_tilde);
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generate_vertex(center, T, inv_T, vec2(-1.0, 1.0), m_tilde, x_tilde, y_tilde, e_tilde);
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generate_vertex(center, T, inv_T, vec2( 1.0, 1.0), m_tilde, x_tilde, y_tilde, e_tilde);
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}
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