/*
* draw()
* - this draws the sprite texture at its current frame of its current animation
* - it positions the sprite based on the transformation formula:
* v' = RotationMatrix*(v-center) + position
* where position is the bottom left corner of the sprite
* and v is each corner of the sprite rectangle, v' is the transformed corner
* and RotationMatrix is defined by the sprite's theta value (counter clockwise)
*/
void TextureSprite::draw(Vector2D camera)
{
if (!visible) return;
glEnable(GL_TEXTURE_2D); // turn on texturing
/* draw the sprite */
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA,GL_ONE_MINUS_SRC_ALPHA);
glPushMatrix();
/* create the drawing tranformation matrix */
Matrix2x2 matrix(1, 0, 0, 1); // identity matrix
if (flipped) matrix *= Matrix2x2(-1, 0, 0, 1); // if the image is flipped, multiply by a horizontal reflection matrix
matrix *= Matrix2x2(cos(theta), sin(theta), -sin(theta), cos(theta)); // multiply by a rotation matrix
/* find pixel location */
Vector2D screenPos = position + center - getScrollMatrix() * camera; // scrollMatrix is used for parallax scrolling
/* find the corner points of the image */
Vector2D p00 = (matrix * Vector2D(-center.x, -center.y)) + screenPos;
Vector2D p01 = (matrix * Vector2D(-center.x, sz.height - center.y)) + screenPos;
Vector2D p10 = (matrix * Vector2D(sz.width - center.x, sz.height - center.y)) + screenPos;
Vector2D p11 = (matrix * Vector2D(sz.width - center.x, -center.y)) + screenPos;
/* get the texture coordinate from the sprite so we know which frame to draw */
SpriteAnimation *anim = animations[currentAnimation];
int currentFrame = anim->currentFrame;
float u,v;
u = anim->coords[currentFrame]->u;
v = anim->coords[currentFrame]->v;
glColor3f(1,1,1);
/* bind the appropriate texture frame */
glBindTexture(GL_TEXTURE_2D,sheet.textureID);
/* Make texture scaling pixelly */
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
/* draw the image as a quad the size of the first loaded image */
glBegin(GL_QUADS);
glTexCoord2f(u,v);
glVertex3f(p00.x,p00.y,0);
glTexCoord2f(u,v+sz.normalizedHeight);
glVertex3f(p01.x,p01.y,0);
glTexCoord2f(u+sz.normalizedWidth,v+sz.normalizedHeight);
glVertex3f(p10.x,p10.y,0);
glTexCoord2f(u+sz.normalizedWidth,v);
glVertex3f(p11.x,p11.y,0);
glEnd();
glPopMatrix();
glDisable(GL_BLEND);
glDisable(GL_TEXTURE_2D);
}
a2de::Matrix3x3 Matrix3x3::Inverse(const Matrix3x3& mat) {
//Minors, Cofactors, Adjugates method.
//See http://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html
//[00 01 02] [0 1 2]
//[10 11 12] [3 4 5]
//[20 21 22] [6 7 8]
//Calculate minors
double m00 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[4], mat._indicies[5], mat._indicies[7], mat._indicies[8]));
double m01 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[3], mat._indicies[5], mat._indicies[6], mat._indicies[7]));
double m02 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[3], mat._indicies[4], mat._indicies[6], mat._indicies[7]));
double m10 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[1], mat._indicies[2], mat._indicies[7], mat._indicies[8]));
double m11 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[0], mat._indicies[2], mat._indicies[6], mat._indicies[7]));
double m12 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[0], mat._indicies[1], mat._indicies[6], mat._indicies[7]));
double m20 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[1], mat._indicies[2], mat._indicies[4], mat._indicies[5]));
double m21 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[0], mat._indicies[2], mat._indicies[3], mat._indicies[5]));
double m22 = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[0], mat._indicies[1], mat._indicies[3], mat._indicies[4]));
Matrix3x3 cofactors(m00, -m01, m02,
-m10, m11, -m12,
m20, -m21, m22);
Matrix3x3 adjugate(Matrix3x3::Transpose(cofactors));
double det_mat = mat.CalculateDeterminant();
double inv_det = 1.0 / det_mat;
return inv_det * adjugate;
}
double Matrix3x3::CalculateDeterminant(const Matrix3x3& mat) {
//a b
//c d
//ad - bc
double a = mat._indicies[0];
double det_not_a = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[4], mat._indicies[5], mat._indicies[7], mat._indicies[8]));
double b = mat._indicies[1];
double det_not_b = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[3], mat._indicies[5], mat._indicies[6], mat._indicies[8]));
double c = mat._indicies[2];
double det_not_c = Matrix2x2::CalculateDeterminant(Matrix2x2(mat._indicies[3], mat._indicies[4], mat._indicies[6], mat._indicies[7]));
return (a * det_not_a) - (b * det_not_b) + (c * det_not_c);
}
const Matrix2x2 transpose(const Matrix2x2& m)
{
return Matrix2x2(
m.m00, m.m10,
m.m01, m.m11
);
}
const Matrix2x2 Matrix2x2::rotation(const float rotation)
{
const float c = Math::cos(rotation);
const float s = Math::sin(rotation);
return Matrix2x2(c, s, -s, c);
}
Matrix2x2 Matrix2x2::Add(Matrix2x2 matrix)
{
return Matrix2x2(
(this->M00 + matrix.M00), (this->M10 + matrix.M10),
(this->M01 + matrix.M01), (this->M11 + matrix.M11)
);
}
Matrix2x2 Matrix2x2::Substract(Matrix2x2 matrix)
{
return Matrix2x2(
(this->M00 - matrix.M00), (this->M10 - matrix.M10),
(this->M01 - matrix.M01), (this->M11 - matrix.M11)
);
}
const Matrix2x2 operator *(const float k, const Matrix2x2& m)
{
return Matrix2x2(
k * m.m00, k * m.m01,
k * m.m10, k * m.m11
);
}
const Matrix2x2 operator -(const Matrix2x2& a, const Matrix2x2& b)
{
return Matrix2x2(
a.m00 - b.m00, a.m01 - b.m01,
a.m10 - b.m10, a.m11 - b.m11
);
}
const Matrix2x2 operator -(const Matrix2x2& m)
{
return Matrix2x2(
-m.m00, -m.m01,
-m.m10, -m.m11
);
}
const Matrix2x2 operator +(const Matrix2x2& a, const Matrix2x2& b)
{
return Matrix2x2(
a.m00 + b.m00, a.m01 + b.m01,
a.m10 + b.m10, a.m11 + b.m11
);
}
const Matrix2x2 Matrix2x2::identity()
{
return Matrix2x2(
1.0f, 0.0f,
0.0f, 1.0f
);
}
Matrix2x2 Matrix2x2::Adjugate()
{
return Matrix2x2(
M11, -M10,
-M01, M00
);
}
Matrix2x2 operator*(const Matrix2x2 &lhs, const Matrix2x2 &rhs) {
Matrix2x2 matrix = Matrix2x2();
matrix.set(0, 0, lhs.get(0, 0) * rhs.get(0, 0) + lhs.get(0, 1) * rhs.get(1, 0));
matrix.set(0, 1, lhs.get(0, 0) * rhs.get(0, 1) + lhs.get(0, 1) * rhs.get(1, 1));
matrix.set(1, 0, lhs.get(1, 0) * rhs.get(0, 0) + lhs.get(1, 1) * rhs.get(1, 0));
matrix.set(1, 1, lhs.get(1, 0) * rhs.get(0, 1) + lhs.get(1, 1) * rhs.get(1, 1));
return matrix;
}
Matrix2x2 Matrix2x2::inverse() const {
double d = det();
if (d == 0)
throw std::invalid_argument("Determinant is 0, so no inverse exists.");
double factor = 1 / d;
return Matrix2x2(get(1, 1) * factor, -get(0, 1) * factor,
-get(1, 0) * factor, get(0, 0) * factor);
}
Matrix2x2 Matrix2x2::inverse()
{
double det = 1 / determinant();
double i11 = det * m22;
double i12 = det * -m12;
double i21 = det * -m21;
double i22 = det * m11;
return Matrix2x2(i11, i12, i21, i22);
}
const Matrix2x2 timesTranspose(const Matrix2x2& a, const Matrix2x2& b)
{
return Matrix2x2(
a.m00 * b.m00 + a.m01 * b.m01,
a.m00 * b.m10 + a.m01 * b.m11,
a.m10 * b.m00 + a.m11 * b.m01,
a.m10 * b.m10 + a.m11 * b.m11
);
}
const Matrix2x2 operator *(const Matrix2x2& a, const Matrix2x2& b)
{
return Matrix2x2(
a.m00 * b.m00 + a.m01 * b.m10,
a.m00 * b.m01 + a.m01 * b.m11,
a.m10 * b.m00 + a.m11 * b.m10,
a.m10 * b.m01 + a.m11 * b.m11
);
}
const Matrix2x2 operator /(const Matrix2x2& m, const float k)
{
// TODO: use tolerances instead of exact values?
GEOMETRY_RUNTIME_ASSERT(k != 0.0f);
return Matrix2x2(
m.m00 / k, m.m01 / k,
m.m10 / k, m.m11 / k
);
}
const Matrix2x2 transposeTimes(const Matrix2x2& a, const Matrix2x2& b)
{
return Matrix2x2(
a.m00 * b.m00 + a.m10 * b.m10,
a.m00 * b.m01 + a.m10 * b.m11,
a.m01 * b.m00 + a.m11 * b.m10,
a.m01 * b.m01 + a.m11 * b.m11
);
}
Ougi::Matrix2x2 Ougi::Matrix2x2::operator*(const Ougi::Matrix2x2& multiplier) const
{
return Matrix2x2(
(matrix[0][0] * multiplier[0][0]) + (matrix[0][1] * multiplier[1][0]),
(matrix[0][0] * multiplier[0][1]) + (matrix[0][1] * multiplier[1][1]),
(matrix[1][0] * multiplier[0][0]) + (matrix[1][1] * multiplier[1][0]),
(matrix[1][0] * multiplier[0][1]) + (matrix[1][1] * multiplier[1][1])
);
}
Matrix2x2 Matrix2x2::Multiply(Matrix2x2 matrix)
{
Vector2 m1r0 = Vector2(this->M00, this->M10);
Vector2 m1r1 = Vector2(this->M01, this->M11);
Vector2 m2r0 = Vector2(matrix.M00, matrix.M01);
Vector2 m2r1 = Vector2(matrix.M10, matrix.M11);
return Matrix2x2(
Vector2::Dot(m1r0,m2r0), Vector2::Dot(m1r0,m2r1),
Vector2::Dot(m1r1,m1r1), Vector2::Dot(m1r1,m2r1)
);
}
const Matrix2x2 orthogonalize(const Matrix2x2& m)
{
// TODO: In the worst case scenario, this could construct a matrix where
// one or both rows are incorrectly set to Vector2(1.0f, 0.0f) because of
// how normalize(const Vector2&) is implemented. Should this function check
// for division by zero instead of relying on the default behavior of
// vector normalization?
const Vector2 x = normalize(m.row(0));
Vector2 y = m.row(1);
// extract the part that is parallel to x and normalize
y -= x * dot(y, x);
y = normalize(y);
return Matrix2x2(x, y);
}
#include "Core/Matrix2x2.h"
#pragma region Vars
Matrix2x2 Matrix2x2::Identity = Matrix2x2(
1, 0,
0, 1
);
#pragma endregion
#pragma region Init
Matrix2x2::Matrix2x2(void)
{
}
Matrix2x2::Matrix2x2(
float m00, float m10,
float m01, float m11
) : M00(m00), M10(m10),
M01(m01), M11(m11)
{
}
Matrix2x2::Matrix2x2(Vector2 v1, Vector2 v2)
: M00(v1.X), M10(v2.X),
M01(v1.Y), M11(v2.Y)
{
}
Matrix2x2::~Matrix2x2(void)
{
//! Subtraction of 2x2 matrices
__device__ Matrix2x2 operator-( const Matrix2x2& b ) const
{
return (Matrix2x2( *this ) -= b );
}