/**
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* Computes a 3x3 rotation matrix that transforms vectors from an ellipsoid's east-north-up coordinate system
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* to eye coordinates. In east-north-up coordinates, x points east, y points north, and z points along the
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* surface normal. East-north-up can be used as an ellipsoid's tangent space for operations such as bump mapping.
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* <br /><br />
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* The ellipsoid is assumed to be centered at the model coordinate's origin.
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*
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* @name czm_eastNorthUpToEyeCoordinates
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* @glslFunction
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*
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* @param {vec3} positionMC The position on the ellipsoid in model coordinates.
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* @param {vec3} normalEC The normalized ellipsoid surface normal, at <code>positionMC</code>, in eye coordinates.
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*
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* @returns {mat3} A 3x3 rotation matrix that transforms vectors from the east-north-up coordinate system to eye coordinates.
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*
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* @example
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* // Transform a vector defined in the east-north-up coordinate
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* // system, (0, 0, 1) which is the surface normal, to eye
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* // coordinates.
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* mat3 m = czm_eastNorthUpToEyeCoordinates(positionMC, normalEC);
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* vec3 normalEC = m * vec3(0.0, 0.0, 1.0);
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*/
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mat3 czm_eastNorthUpToEyeCoordinates(vec3 positionMC, vec3 normalEC)
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{
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vec3 tangentMC = normalize(vec3(-positionMC.y, positionMC.x, 0.0)); // normalized surface tangent in model coordinates
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vec3 tangentEC = normalize(czm_normal3D * tangentMC); // normalized surface tangent in eye coordiantes
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vec3 bitangentEC = normalize(cross(normalEC, tangentEC)); // normalized surface bitangent in eye coordinates
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return mat3(
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tangentEC.x, tangentEC.y, tangentEC.z,
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bitangentEC.x, bitangentEC.y, bitangentEC.z,
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normalEC.x, normalEC.y, normalEC.z);
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}
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