ic
/
magnum
mirror of https://github.com/mosra/magnum.git
6
0
Fork 0
Code Issues Projects Releases Wiki Activity
Browse Source

Math: support infinite far plane in Matrix::perspectiveProjection().

pull/179/head
Vladimír Vondruš 10 years ago
parent
9fdf467c59
commit
87074202c8
2 changed files with 65 additions and 12 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 39
      src/Magnum/Math/Matrix4.h
  2. 28
      src/Magnum/Math/Test/Matrix4Test.cpp

39
src/Magnum/Math/Matrix4.h
Unescape View File

@ -281,7 +281,7 @@ template<class T> class Matrix4: public Matrix4x4<T> {
* @param near Distance to near clipping plane, positive is ahead
* @param far Distance to far clipping plane, positive is ahead
*
* @f[
* If @p far is finite, the result is: @f[
* \boldsymbol{A} = \begin{pmatrix}
* \frac{2n}{s_x} & 0 & 0 & 0 \\
* 0 & \frac{2n}{s_y} & 0 & 0 \\
@ -289,7 +289,17 @@ template<class T> class Matrix4: public Matrix4x4<T> {
* 0 & 0 & -1 & 0
* \end{pmatrix}
* @f]
* @see @ref orthographicProjection(), @ref Matrix3::projection()
*
* For infinite @p far, the result is: @f[
* \boldsymbol{A} = \begin{pmatrix}
* \frac{2n}{s_x} & 0 & 0 & 0 \\
* 0 & \frac{2n}{s_y} & 0 & 0 \\
* 0 & 0 & -1 & -2n \\
* 0 & 0 & -1 & 0
* \end{pmatrix}
* @f]
* @see @ref orthographicProjection(), @ref Matrix3::projection(),
* @ref Constants::inf()
*/
static Matrix4<T> perspectiveProjection(const Vector2<T>& size, T near, T far);
@ -300,7 +310,7 @@ template<class T> class Matrix4: public Matrix4x4<T> {
* @param near Near clipping plane
* @param far Far clipping plane
*
* @f[
* If @p far is finite, the result is: @f[
* \boldsymbol{A} = \begin{pmatrix}
* \frac{1}{\tan{\frac{\theta}{2}}} & 0 & 0 & 0 \\
* 0 & \frac{a}{\tan{\frac{\theta}{2}}} & 0 & 0 \\
@ -308,7 +318,17 @@ template<class T> class Matrix4: public Matrix4x4<T> {
* 0 & 0 & -1 & 0
* \end{pmatrix}
* @f]
* @see @ref orthographicProjection(), @ref Matrix3::projection()
*
* For infinite @p far, the result is: @f[
* \boldsymbol{A} = \begin{pmatrix}
* \frac{1}{\tan{\frac{\theta}{2}}} & 0 & 0 & 0 \\
* 0 & \frac{a}{\tan{\frac{\theta}{2}}} & 0 & 0 \\
* 0 & 0 & -1 & -2n \\
* 0 & 0 & -1 & 0
* \end{pmatrix}
* @f]
* @see @ref orthographicProjection(), @ref Matrix3::projection(),
* @ref Constants::inf()
*/
static Matrix4<T> perspectiveProjection(Rad<T> fov, T aspectRatio, T near, T far) {
const T xyScale = 2*std::tan(T(fov)/2)*near;
@ -640,13 +660,20 @@ template<class T> Matrix4<T> Matrix4<T>::orthographicProjection(const Vector2<T>
}
template<class T> Matrix4<T> Matrix4<T>::perspectiveProjection(const Vector2<T>& size, const T near, const T far) {
Vector2<T> xyScale = 2*near/size;
T zScale = T(1.0)/(near-far);
const Vector2<T> xyScale = 2*near/size;
if(far == Constants<T>::inf()) {
return {{xyScale.x(), T(0), T(0), T(0)},
{ T(0), xyScale.y(), T(0), T(0)},
{ T(0), T(0), T(-1), T(-1)},
{ T(0), T(0), T(-2)*near, T(0)}};
} else {
const T zScale = T(1.0)/(near-far);
return {{xyScale.x(), T(0), T(0), T(0)},
{ T(0), xyScale.y(), T(0), T(0)},
{ T(0), T(0), (far+near)*zScale, T(-1)},
{ T(0), T(0), T(2)*far*near*zScale, T(0)}};
}
}
template<class T> Matrix4<T> Matrix4<T>::lookAt(const Vector3<T>& eye, const Vector3<T>& target, const Vector3<T>& up) {

28
src/Magnum/Math/Test/Matrix4Test.cpp
Unescape View File

@ -84,7 +84,9 @@ struct Matrix4Test: Corrade::TestSuite::Tester {
void shearingYZ();
void orthographicProjection();
void perspectiveProjection();
void perspectiveProjectionInfiniteFar();
void perspectiveProjectionFov();
void perspectiveProjectionFovInfiniteFar();
void lookAt();
void fromParts();
@ -134,7 +136,9 @@ Matrix4Test::Matrix4Test() {
&Matrix4Test::shearingYZ,
&Matrix4Test::orthographicProjection,
&Matrix4Test::perspectiveProjection,
&Matrix4Test::perspectiveProjectionInfiniteFar,
&Matrix4Test::perspectiveProjectionFov,
&Matrix4Test::perspectiveProjectionFovInfiniteFar,
&Matrix4Test::lookAt,
&Matrix4Test::fromParts,
@ -420,12 +424,34 @@ void Matrix4Test::perspectiveProjection() {
CORRADE_COMPARE(actual.transformPoint({0.0f, 0.0f, -100.0f}), Vector3(0.0f, 0.0f, +1.0f));
}
void Matrix4Test::perspectiveProjectionInfiniteFar() {
Matrix4 expected({4.0f, 0.0f, 0.0f, 0.0f},
{0.0f, 7.111111f, 0.0f, 0.0f},
{0.0f, 0.0f, -1.0f, -1.0f},
{0.0f, 0.0f, -64.0f, 0.0f});
Matrix4 actual = Matrix4::perspectiveProjection({16.0f, 9.0f}, 32.0f, Constants::inf());
CORRADE_COMPARE(actual, expected);
/* NDC is left-handed, so point on near plane should be -1 and a *vector*
in direction of far plane +1 */
CORRADE_COMPARE(actual.transformPoint({0.0f, 0.0f, -32.0f}), Vector3(0.0f, 0.0f, -1.0f));
CORRADE_COMPARE(actual.transformVector({0.0f, 0.0f, -1.0f}), Vector3(0.0f, 0.0f, +1.0f));
}
void Matrix4Test::perspectiveProjectionFov() {
Matrix4 expected({4.1652994f, 0.0f, 0.0f, 0.0f},
{ 0.0f, 9.788454f, 0.0f, 0.0f},
{ 0.0f, 0.0f, -1.9411764f, -1.0f},
{ 0.0f, 0.0f, -94.1176452f, 0.0f});
CORRADE_COMPARE(Matrix4::perspectiveProjection(Deg(27.0f), 2.35f, 32.0f, 100), expected);
CORRADE_COMPARE(Matrix4::perspectiveProjection(Deg(27.0f), 2.35f, 32.0f, 100.0f), expected);
}
void Matrix4Test::perspectiveProjectionFovInfiniteFar() {
Matrix4 expected({4.1652994f, 0.0f, 0.0f, 0.0f},
{ 0.0f, 9.788454f, 0.0f, 0.0f},
{ 0.0f, 0.0f, -1.0f, -1.0f},
{ 0.0f, 0.0f, -64.0f, 0.0f});
CORRADE_COMPARE(Matrix4::perspectiveProjection(Deg(27.0f), 2.35f, 32.0f, Constants::inf()), expected);
}
void Matrix4Test::fromParts() {

Write Preview
Loading…
Cancel
Save