我们发现HP的打印机驱动程序无法正常处理许多打印机的PlgBlt（）。
我们的目的是自己处理任何正交旋转，并且只有打印机处理比例和平移（它似乎正确处理）。
我在代码中可以使用2D矩阵，我将把位图“绘制”到打印机的DC。
我在数学方面很弱，而且我对矩阵数学有足够的了解，可以用它来转换2D或3D坐标。但基础数学对我来说是不透明的。
所以，我需要的是检测给定的2D矩阵在其变换中是否正交（无论如何都是旋转方面）。我想另一种问这个问题的方法是：如何将旋转矢量从2D矩阵中取出？如果我知道以弧度或度数表示的旋转角度，我可以说它的正交与否（0,90,180,270）。
据推测，代码在这个主题上是通用的，但下面是我们使用的代码的基础知识，如果有帮助的话：
typedef double ThreeByThreeMatrix[3][3]; // 3x3 for an X, Y coordinate transformation matrix
然后有一个处理最明显操作的包装器：
class Simple2DTransform
{
public:
////////////////////////////////////////////////////
// Construction
////////////////////////////////////////////////////
// we always begin life as an identity matrix (you can then apply scale, skew, etc.)
Simple2DTransform()
{
Reset();
}
////////////////////////////////////////////////////
// Operators
////////////////////////////////////////////////////
bool operator == (const Simple2DTransform & rhs) const
{
return memcmp(m_matrix, rhs.m_matrix, sizeof(m_matrix)) == 0;
}
Simple2DTransform & operator *= (const Simple2DTransform & rhs)
{
return *this = GetCrossProduct(rhs);
}
////////////////////////////////////////////////////
// Setup
////////////////////////////////////////////////////
// reset to the identity matrix
Simple2DTransform & Reset()
{
memcpy(m_matrix, GetIdentityMatrix(), sizeof(m_matrix));
return *this;
}
// combine with the specified translation
Simple2DTransform & Translate(double x_shift, double y_shift)
{
Simple2DTransform transform;
translate(x_shift, y_shift, transform.m_matrix);
return *this *= transform;
}
// combine with the specified operations (these are cumulative operations, so rotating twice by 1 degree gives a total of 2 degrees rotation)
Simple2DTransform & Rotate(double radians)
{
Simple2DTransform transform;
rotate(radians, transform.m_matrix);
return *this *= transform;
}
// apply a heterogeneous scale factor
Simple2DTransform & Scale(double x_scale, double y_scale)
{
Simple2DTransform transform;
scale(x_scale, y_scale, transform.m_matrix);
return *this *= transform;
}
// apply a homogeneous scale factor
Simple2DTransform & Scale(double scale)
{
return Scale(scale, scale);
}
// apply a skew
Simple2DTransform & Skew(double skew)
{
Simple2DTransform transform;
skew_y(skew, transform.m_matrix);
return *this *= transform;
}
////////////////////////////////////////////////////
// Queries
////////////////////////////////////////////////////
// return the cross product of this and the given matrix
Simple2DTransform GetCrossProduct(const Simple2DTransform & rhs) const
{
Simple2DTransform result;
GEMM(m_matrix, rhs.m_matrix, result.m_matrix);
return result;
}
// returns the inverse of ourselves
Simple2DTransform GetInverse() const
{
// note: invert mucks with both matrices, so we use a copy of ourselves for it
Simple2DTransform original(*this), inverse;
invert(original.m_matrix, inverse.m_matrix);
return inverse;
}
// derivative values
double GetCoefficient(int i, int j) const
{
return m_matrix[i][j];
}
// return the cross product
double GetDeterminate() const
{
return m_matrix[0][0]*m_matrix[1][1] - m_matrix[0][1]*m_matrix[1][0];
}
// returns the square root of the determinate (this ignores heterogeneous scaling factors)
double GetScale() const
{
return sqrt(abs(GetDeterminate()));
}
// returns true if there is a scale factor
bool IsStretched() const
{
return (abs(abs(m_matrix[0][0]) - abs(m_matrix[1][1])) > 1.0e-7
|| abs(abs(m_matrix[0][1]) - abs(m_matrix[1][0])) > 1.0e-7);
}
// true if we're the identity matrix
bool IsIdentity() const
{
return memcmp(m_matrix, GetIdentityMatrix(), sizeof(m_matrix)) == 0;
}
// returns true if this represents the same transformation as the given subtable
bool IsSubtableEqual(const SUBTABLE * pSubTable) const
{
ASSERT(pSubTable);
if (abs(pSubTable->tran1 - m_matrix[0][0]) > 1.0e-7)
return false;
if (abs(pSubTable->tran2 - m_matrix[1][0]) > 1.0e-7)
return false;
if (abs(pSubTable->tran3 - m_matrix[0][1]) > 1.0e-7)
return false;
if (abs(pSubTable->tran4 - m_matrix[1][1]) > 1.0e-7)
return false;
return true;
}
////////////////////////////////////////////////////
// Application / Execution
////////////////////////////////////////////////////
void Transform(const SimplePoint & point, SimplePoint & newpoint) const
{
newpoint.x = point.x * m_matrix[0][0] + point.y * m_matrix[1][0] + m_matrix[2][0];
newpoint.y = point.x * m_matrix[0][1] + point.y * m_matrix[1][1] + m_matrix[2][1];
}
void Transform(SimplePoint & point) const
{
SimplePoint newpoint;
Transform(point, newpoint);
point = newpoint;
}
void Transform(const SimpleRect & rect, SimpleRect & newrect) const
{
newrect.minX = rect.minX * m_matrix[0][0] + rect.minY * m_matrix[1][0] + m_matrix[2][0];
newrect.minY = rect.minX * m_matrix[0][1] + rect.minY * m_matrix[1][1] + m_matrix[2][1];
newrect.maxX = rect.maxX * m_matrix[0][0] + rect.maxY * m_matrix[1][0] + m_matrix[2][0];
newrect.maxY = rect.maxX * m_matrix[0][1] + rect.maxY * m_matrix[1][1] + m_matrix[2][1];
}
void Transform(SimpleRect & rect) const
{
SimpleRect newrect;
Transform(rect, newrect);
rect = newrect;
}
void Transform(CPoint & point) const
{
SimplePoint newpoint(point);
Transform(newpoint);
point.x = (int)(newpoint.x > 0.0 ? newpoint.x + 0.5 : newpoint.x - 0.5);
point.y = (int)(newpoint.y > 0.0 ? newpoint.y + 0.5 : newpoint.y - 0.5);
}
void Transform(SimplePoint point, CPoint & transformed) const
{
Transform(point);
transformed.x = (int)(point.x > 0.0 ? point.x + 0.5 : point.x - 0.5);
transformed.y = (int)(point.y > 0.0 ? point.y + 0.5 : point.y - 0.5);
}
void Transform(CPoint point, SimplePoint & transformed) const
{
transformed = point;
Transform(transformed);
}
void Transform(double dx, double dy, double & x, double & y) const
{
SimplePoint point(dx, dy);
Transform(point);
x = point.x;
y = point.y;
}
void Transform(double & x, double & y) const
{
SimplePoint point(x, y);
Transform(point);
x = point.x;
y = point.y;
}
SimplePoint GetTransformed(SimplePoint point) const
{
Transform(point);
return point;
}
CPoint GetTransformed(CPoint point) const
{
Transform(point);
return point;
}
SimpleRect GetTransformed(const CRect & rect) const
{
return SimpleRect(GetTransformed(SimplePoint(rect.left, rect.bottom)), GetTransformed(SimplePoint(rect.right, rect.top)));
}
SimpleRect GetTransformed(double x1, double y1, double x2, double y2) const
{
return SimpleRect(GetTransformed(SimplePoint(x1, y1)), GetTransformed(SimplePoint(x2, y2)));
}
double GetTransformedX(double x, double y) const
{
return GetTransformed(SimplePoint(x, y)).x;
}
double GetTransformedY(double x, double y) const
{
return GetTransformed(SimplePoint(x, y)).y;
}
double GetTransformedX(int x, int y) const
{
return GetTransformed(SimplePoint(x, y)).x;
}
double GetTransformedY(int x, int y) const
{
return GetTransformed(SimplePoint(x, y)).y;
}
double GetTransformedX(const SimplePoint & point) const
{
return GetTransformed(point).x;
}
double GetTransformedY(const SimplePoint & point) const
{
return GetTransformed(point).y;
}
int GetTransformedIntX(double x, double y) const
{
CPoint point;
Transform(SimplePoint(x, y), point);
return point.x;
}
int GetTransformedIntY(double x, double y) const
{
CPoint point;
Transform(SimplePoint(x, y), point);
return point.y;
}
int GetTransformedIntX(const SimplePoint & point) const
{
CPoint pt;
Transform(point, pt);
return pt.x;
}
int GetTransformedIntY(const SimplePoint & point) const
{
CPoint pt;
Transform(point, pt);
return pt.y;
}
protected:
////////////////////////////////////////////////////
// Static Class Operations
////////////////////////////////////////////////////
static const ThreeByThreeMatrix & GetIdentityMatrix();
////////////////////////////////////////////////////
// Instance Variables
////////////////////////////////////////////////////
ThreeByThreeMatrix m_matrix;
};
答案 0 :(得分：2)
设A =（0,0），B =（1,0）。通过矩阵转换得到A'和B'。测量矢量B' - A'的角度。这应该给你角度。
要测量矢量的角度，您可以使用atan2（B'.y - A'.y，B'.x - A'.x）