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62 lines
3.4 KiB
GLSL
62 lines
3.4 KiB
GLSL
/*****************************************************************************************
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* *
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* OpenSpace *
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* *
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* Copyright (c) 2014-2025 *
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* *
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* Permission is hereby granted, free of charge, to any person obtaining a copy of this *
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* software and associated documentation files (the "Software"), to deal in the Software *
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* without restriction, including without limitation the rights to use, copy, modify, *
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* merge, publish, distribute, sublicense, and/or sell copies of the Software, and to *
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* permit persons to whom the Software is furnished to do so, subject to the following *
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* conditions: *
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* *
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* The above copyright notice and this permission notice shall be included in all copies *
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* or substantial portions of the Software. *
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* *
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, *
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* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A *
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* PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT *
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* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF *
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* CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE *
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* OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. *
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****************************************************************************************/
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bool rayIntersectsEllipsoid(vec3 rayOrigin, vec3 rayDir, vec3 ellipsoidCenter,
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vec3 ellipsoidRadii)
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{
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// Translate ray to ellipsoid's local coordinate system
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vec3 oc = rayOrigin - ellipsoidCenter;
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// Normalize by ellipsoid radii to convert to unit sphere problem
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vec3 ocNorm = oc / ellipsoidRadii;
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vec3 dirNorm = rayDir / ellipsoidRadii;
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// Quadratic equation coefficients: A*t^2 + B*t + C = 0
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float a = dot(dirNorm, dirNorm);
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float b = dot(ocNorm, dirNorm); // Note: factor of 2 moved to discriminant calc
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float c = dot(ocNorm, ocNorm) - 1.0;
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// Calculate discriminant (optimized: b^2 - ac since we factored out the 2)
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float discriminant = b * b - a * c;
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// Early exit if no intersection
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if (discriminant < 0.0) {
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return false;
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}
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// Check if at least one intersection is in front of ray origin
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// For quadratic A*t^2 + 2*B*t + C = 0, if we want to check if any t >= 0:
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// If C <= 0, ray origin is inside ellipsoid, so definitely intersects
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if (c <= 0.0) {
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return true;
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}
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// If both intersections exist and C > 0, check if the smaller root t1 >= 0
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// t1 = (-b - sqrt(discriminant)) / a
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// Since we need t1 >= 0: -b - sqrt(discriminant) >= 0
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// This means: -b >= sqrt(discriminant), so b <= -sqrt(discriminant)
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// Since sqrt(discriminant) >= 0, this means b <= 0
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return b <= 0.0;
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}
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