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Fix precision loss on small angles in qua's pow

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This commit is contained in:
Quentin Santos 2019-08-31 19:36:20 +02:00
parent 9ca99751f0
commit c597094980
4 changed files with 33 additions and 6 deletions
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28
glm/ext/quaternion_exponential.inl
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@ -1,3 +1,5 @@
#include "scalar_constants.hpp"
namespace glm namespace glm
{ {
template<typename T, qualifier Q> template<typename T, qualifier Q>
@ -46,16 +48,30 @@ namespace glm
//To deal with non-unit quaternions //To deal with non-unit quaternions
T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w); T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w);
//Equivalent to raising a real number to a power T Angle;
//Needed to prevent a division by 0 error later on if(abs(x.w / magnitude) > cos_one_over_two<T>())
if(abs(x.w / magnitude) > static_cast<T>(1) - epsilon<T>() && abs(x.w / magnitude) < static_cast<T>(1) + epsilon<T>()) {
return qua<T, Q>(pow(x.w, y), 0, 0, 0); //Scalar component is close to 1; using it to recover angle would lose precision
//Instead, we use the non-scalar components since sin() is accurate around 0
//Prevent a division by 0 error later on
T VectorMagnitude = x.x * x.x + x.y * x.y + x.z * x.z;
if (glm::abs(VectorMagnitude - static_cast<T>(0)) < glm::epsilon<T>()) {
//Equivalent to raising a real number to a power
return qua<T, Q>(pow(x.w, y), 0, 0, 0);
}
Angle = asin(sqrt(VectorMagnitude) / magnitude);
}
else
{
//Scalar component is small, shouldn't cause loss of precision
Angle = acos(x.w / magnitude);
}
T Angle = acos(x.w / magnitude);
T NewAngle = Angle * y; T NewAngle = Angle * y;
T Div = sin(NewAngle) / sin(Angle); T Div = sin(NewAngle) / sin(Angle);
T Mag = pow(magnitude, y - static_cast<T>(1)); T Mag = pow(magnitude, y - static_cast<T>(1));
return qua<T, Q>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag); return qua<T, Q>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
} }

4
glm/ext/scalar_constants.hpp
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@ -30,6 +30,10 @@ namespace glm
template<typename genType> template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR genType pi(); GLM_FUNC_DECL GLM_CONSTEXPR genType pi();
/// Return the value of cos(1 / 2) for floating point types.
template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR genType cos_one_over_two();
/// @} /// @}
} //namespace glm } //namespace glm

6
glm/ext/scalar_constants.inl
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@ -15,4 +15,10 @@ namespace glm
GLM_STATIC_ASSERT(std::numeric_limits<genType>::is_iec559, "'pi' only accepts floating-point inputs"); GLM_STATIC_ASSERT(std::numeric_limits<genType>::is_iec559, "'pi' only accepts floating-point inputs");
return static_cast<genType>(3.14159265358979323846264338327950288); return static_cast<genType>(3.14159265358979323846264338327950288);
} }
template<typename genType>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR genType cos_one_over_two()
{
return genType(0.877582561890372716130286068203503191);
}
} //namespace glm } //namespace glm

1
glm/gtc/constants.inl
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@ -163,4 +163,5 @@ namespace glm
{ {
return genType(1.61803398874989484820458683436563811); return genType(1.61803398874989484820458683436563811);
} }
} //namespace glm } //namespace glm