/**
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* DOC_TBA
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*
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* @name czm_rayEllipsoidIntersectionInterval
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* @glslFunction
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*/
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czm_raySegment czm_rayEllipsoidIntersectionInterval(czm_ray ray, vec3 ellipsoid_center, vec3 ellipsoid_inverseRadii)
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{
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// ray and ellipsoid center in eye coordinates. radii in model coordinates.
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vec3 q = ellipsoid_inverseRadii * (czm_inverseModelView * vec4(ray.origin, 1.0)).xyz;
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vec3 w = ellipsoid_inverseRadii * (czm_inverseModelView * vec4(ray.direction, 0.0)).xyz;
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q = q - ellipsoid_inverseRadii * (czm_inverseModelView * vec4(ellipsoid_center, 1.0)).xyz;
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float q2 = dot(q, q);
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float qw = dot(q, w);
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if (q2 > 1.0) // Outside ellipsoid.
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{
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if (qw >= 0.0) // Looking outward or tangent (0 intersections).
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{
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return czm_emptyRaySegment;
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}
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else // qw < 0.0.
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{
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float qw2 = qw * qw;
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float difference = q2 - 1.0; // Positively valued.
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float w2 = dot(w, w);
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float product = w2 * difference;
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if (qw2 < product) // Imaginary roots (0 intersections).
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{
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return czm_emptyRaySegment;
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}
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else if (qw2 > product) // Distinct roots (2 intersections).
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{
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float discriminant = qw * qw - product;
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float temp = -qw + sqrt(discriminant); // Avoid cancellation.
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float root0 = temp / w2;
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float root1 = difference / temp;
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if (root0 < root1)
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{
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czm_raySegment i = czm_raySegment(root0, root1);
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return i;
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}
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else
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{
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czm_raySegment i = czm_raySegment(root1, root0);
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return i;
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}
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}
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else // qw2 == product. Repeated roots (2 intersections).
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{
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float root = sqrt(difference / w2);
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czm_raySegment i = czm_raySegment(root, root);
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return i;
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}
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}
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}
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else if (q2 < 1.0) // Inside ellipsoid (2 intersections).
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{
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float difference = q2 - 1.0; // Negatively valued.
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float w2 = dot(w, w);
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float product = w2 * difference; // Negatively valued.
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float discriminant = qw * qw - product;
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float temp = -qw + sqrt(discriminant); // Positively valued.
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czm_raySegment i = czm_raySegment(0.0, temp / w2);
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return i;
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}
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else // q2 == 1.0. On ellipsoid.
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{
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if (qw < 0.0) // Looking inward.
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{
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float w2 = dot(w, w);
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czm_raySegment i = czm_raySegment(0.0, -qw / w2);
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return i;
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}
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else // qw >= 0.0. Looking outward or tangent.
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{
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return czm_emptyRaySegment;
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}
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}
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}
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