CS计算机代考程序代写 ///////////////////////////////////////////////////////////////////////////////////

程序代写 CS代考

///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 – 2015 G-Truc Creation (www.g-truc.net)
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///
/// @ref gtx_matrix_decompose
/// @file glm/gtx/matrix_decompose.inl
/// @date 2014-08-29 / 2014-08-29
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

namespace glm
{
/// Make a linear combination of two vectors and return the result.
// result = (a * ascl) + (b * bscl)
template
GLM_FUNC_QUALIFIER tvec3 combine(
tvec3 const & a,
tvec3 const & b,
T ascl, T bscl)
{
return (a * ascl) + (b * bscl);
}

template
GLM_FUNC_QUALIFIER void v3Scale(tvec3 & v, T desiredLength)
{
T len = glm::length(v);
if(len != 0)
{
T l = desiredLength / len;
v[0] *= l;
v[1] *= l;
v[2] *= l;
}
}

/**
* Matrix decompose
* http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
* Decomposes the mode matrix to translations,rotation scale components
*
*/

template
GLM_FUNC_QUALIFIER bool decompose(tmat4x4 const & ModelMatrix, tvec3 & Scale, tquat & Orientation, tvec3 & Translation, tvec3 & Skew, tvec4 & Perspective)
{
tmat4x4 LocalMatrix(ModelMatrix);

// Normalize the matrix.
if(LocalMatrix[3][3] == static_cast(0))
return false;

for(length_t i = 0; i < 4; ++i) for(length_t j = 0; j < 4; ++j) LocalMatrix[i][j] /= LocalMatrix[3][3]; // perspectiveMatrix is used to solve for perspective, but it also provides // an easy way to test for singularity of the upper 3x3 component. tmat4x4 PerspectiveMatrix(LocalMatrix);

for(length_t i = 0; i < 3; i++) PerspectiveMatrix[i][3] = 0; PerspectiveMatrix[3][3] = 1; /// TODO: Fixme! if(determinant(PerspectiveMatrix) == static_cast(0))
return false;

// First, isolate perspective. This is the messiest.
if(LocalMatrix[0][3] != 0 || LocalMatrix[1][3] != 0 || LocalMatrix[2][3] != 0)
{
// rightHandSide is the right hand side of the equation.
tvec4 RightHandSide;
RightHandSide[0] = LocalMatrix[0][3];
RightHandSide[1] = LocalMatrix[1][3];
RightHandSide[2] = LocalMatrix[2][3];
RightHandSide[3] = LocalMatrix[3][3];

// Solve the equation by inverting PerspectiveMatrix and multiplying
// rightHandSide by the inverse. (This is the easiest way, not
// necessarily the best.)
tmat4x4 InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);// inverse(PerspectiveMatrix, inversePerspectiveMatrix);
tmat4x4 TransposedInversePerspectiveMatrix = glm::transpose(InversePerspectiveMatrix);// transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix);

Perspective = TransposedInversePerspectiveMatrix * RightHandSide;
// v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint);

// Clear the perspective partition
LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = 0;
LocalMatrix[3][3] = 1;
}
else
{
// No perspective.
Perspective = tvec4(0, 0, 0, 1);
}

// Next take care of translation (easy).
Translation = tvec3(LocalMatrix[3]);
LocalMatrix[3] = tvec4(0, 0, 0, LocalMatrix[3].w);

tvec3 Row[3], Pdum3;

// Now get scale and shear.
for(length_t i = 0; i < 3; ++i) for(int j = 0; j < 3; ++j) Row[i][j] = LocalMatrix[i][j]; // Compute X scale factor and normalize first row. Scale.x = length(Row[0]);// v3Length(Row[0]); v3Scale(Row[0], static_cast(1));

// Compute XY shear factor and make 2nd row orthogonal to 1st.
Skew.z = dot(Row[0], Row[1]);
Row[1] = combine(Row[1], Row[0], static_cast(1), -Skew.z);

// Now, compute Y scale and normalize 2nd row.
Scale.y = length(Row[1]);
v3Scale(Row[1], static_cast(1));
Skew.z /= Scale.y;

// Compute XZ and YZ shears, orthogonalize 3rd row.
Skew.y = glm::dot(Row[0], Row[2]);
Row[2] = combine(Row[2], Row[0], static_cast(1), -Skew.y);
Skew.x = glm::dot(Row[1], Row[2]);
Row[2] = combine(Row[2], Row[1], static_cast(1), -Skew.x);

// Next, get Z scale and normalize 3rd row.
Scale.z = length(Row[2]);
v3Scale(Row[2], static_cast(1));
Skew.y /= Scale.z;
Skew.x /= Scale.z;

// At this point, the matrix (in rows[]) is orthonormal.
// Check for a coordinate system flip. If the determinant
// is -1, then negate the matrix and the scaling factors.
Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
if(dot(Row[0], Pdum3) < 0) { for(length_t i = 0; i < 3; i++) { Scale.x *= static_cast(-1);
Row[i] *= static_cast(-1);
}
}

// Now, get the rotations out, as described in the gem.

// FIXME – Add the ability to return either quaternions (which are
// easier to recompose with) or Euler angles (rx, ry, rz), which
// are easier for authors to deal with. The latter will only be useful
// when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I
// will leave the Euler angle code here for now.

// ret.rotateY = asin(-Row[0][2]);
// if (cos(ret.rotateY) != 0) {
// ret.rotateX = atan2(Row[1][2], Row[2][2]);
// ret.rotateZ = atan2(Row[0][1], Row[0][0]);
// } else {
// ret.rotateX = atan2(-Row[2][0], Row[1][1]);
// ret.rotateZ = 0;
// }

T s, t, x, y, z, w;

t = Row[0][0] + Row[1][1] + Row[2][2] + 1.0;

if(t > 1e-4)
{
s = 0.5 / sqrt(t);
w = 0.25 / s;
x = (Row[2][1] – Row[1][2]) * s;
y = (Row[0][2] – Row[2][0]) * s;
z = (Row[1][0] – Row[0][1]) * s;
}
else if(Row[0][0] > Row[1][1] && Row[0][0] > Row[2][2])
{
s = sqrt (1.0 + Row[0][0] – Row[1][1] – Row[2][2]) * 2.0; // S=4*qx
x = 0.25 * s;
y = (Row[0][1] + Row[1][0]) / s;
z = (Row[0][2] + Row[2][0]) / s;
w = (Row[2][1] – Row[1][2]) / s;
}
else if(Row[1][1] > Row[2][2])
{
s = sqrt (1.0 + Row[1][1] – Row[0][0] – Row[2][2]) * 2.0; // S=4*qy
x = (Row[0][1] + Row[1][0]) / s;
y = 0.25 * s;
z = (Row[1][2] + Row[2][1]) / s;
w = (Row[0][2] – Row[2][0]) / s;
}
else
{
s = sqrt(1.0 + Row[2][2] – Row[0][0] – Row[1][1]) * 2.0; // S=4*qz
x = (Row[0][2] + Row[2][0]) / s;
y = (Row[1][2] + Row[2][1]) / s;
z = 0.25 * s;
w = (Row[1][0] – Row[0][1]) / s;
}

Orientation.x = x;
Orientation.y = y;
Orientation.z = z;
Orientation.w = w;

return true;
}
}//namespace glm

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