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Radial shading

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Jakub Melka
2021-03-10 19:01:17 +01:00
parent d7ba96ac5b
commit 8ddbcc0f4d
2 changed files with 227 additions and 0 deletions
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223
Pdf4QtLib/sources/pdfpattern.cpp
View File

@@ -1702,6 +1702,229 @@ PDFMesh PDFRadialShading::createMesh(const PDFMeshQualitySettings& settings, con
return mesh;
}
class PDFRadialShadingSampler : public PDFShadingSampler
{
public:
PDFRadialShadingSampler(const PDFRadialShading* radialShadingPattern, QMatrix userSpaceToDeviceSpaceMatrix) :
PDFShadingSampler(radialShadingPattern),
m_radialShadingPattern(radialShadingPattern),
m_xStart(0.0),
m_xEnd(0.0),
m_tAtStart(0.0),
m_tAtEnd(0.0),
m_tMin(0.0),
m_tMax(0.0),
m_r0(0.0),
m_r1(0.0)
{
QMatrix patternSpaceToDeviceSpace = radialShadingPattern->getMatrix() * userSpaceToDeviceSpaceMatrix;
QPointF p1 = patternSpaceToDeviceSpace.map(radialShadingPattern->getStartPoint());
QPointF p2 = patternSpaceToDeviceSpace.map(radialShadingPattern->getEndPoint());
// Strategy: for simplification, we rotate the line clockwise so we will
// get the shading axis equal to the x-axis.
QLineF line(p1, p2);
const double angle = line.angleTo(QLineF(0, 0, 1, 0));
// Matrix p1p2LCS is local coordinate system of line p1-p2. It transforms
// points on the line to the global coordinate system. So, point (0, 0) will
// map onto p1 and point (length(p1-p2), 0) will map onto p2.
QMatrix p1p2LCS;
p1p2LCS.translate(p1.x(), p1.y());
p1p2LCS.rotate(angle);
QMatrix p1p2GCS = p1p2LCS.inverted();
QPointF p1m = p1p2GCS.map(p1);
QPointF p2m = p1p2GCS.map(p2);
Q_ASSERT(isZero(p1m.y()));
Q_ASSERT(isZero(p2m.y()));
Q_ASSERT(p1m.x() <= p2m.x());
m_xStart = p1m.x();
m_xEnd = p2m.x();
m_tAtStart = radialShadingPattern->getDomainStart();
m_tAtEnd = radialShadingPattern->getDomainEnd();
m_tMin = qMin(m_tAtStart, m_tAtEnd);
m_tMax = qMax(m_tAtStart, m_tAtEnd);
m_r0 = radialShadingPattern->getR0();
m_r1 = radialShadingPattern->getR1();
m_p1p2GCS = p1p2GCS;
}
virtual bool sample(const QPointF& devicePoint, PDFColorBuffer outputBuffer, int limit) const override
{
Q_UNUSED(limit);
if (!m_pattern->getColorSpace() || m_pattern->getColorSpace()->getColorComponentCount() != outputBuffer.size())
{
// Invalid color space, or invalid color buffer
return false;
}
QPointF mappedPoint = m_p1p2GCS.map(devicePoint);
// Well, how to proceed with sampling? We would like to find parameter s for point (x_p, y_p),
// where (x_p, y_p) is mappedPoint. According to the formulas in the PDF 2.0 specification, we want
// to find variable s:
//
// x_c = x_0 + s * (x_1 - x_0)
// y_c = y_0 + s * (y_1 - y_0)
// r = r_0 + s * (r_1 - r_0)
//
// Where (x_c, y_c) is center of the circle. We assume this simplification: we translate the pattern
// to horizontal axis, this implies y_0 = y_1 = 0, so y_c will be always zero. This will allow us to use
// simplification.
//
// This is general equation, which we want to solve:
//
// (x_p - x_c)^2 + (y_p - y_c)^2 = r^2,
// where (x_p, y_p) is sample point, (x_c, y_c) is coordinate of the circle center and r is radius.
// If we use y_c = 0, then we get following equation:
//
// (x_p - x_c)^2 + y_p^2 = r^2,
//
// If we substitute x_c and r with formulas above, we get:
//
// (x_p - x_0 - s * (x_1 - x_0))^2 + y_p^2 = (r_0 + s * (r_1 - r_0))^2,
//
// We also have x_0 = 0, because we have origin at (0, 0), so we get following final equation:
//
// (x_p - s * x_1)^2 + y_p^2 = (r_0 + s * (r_1 - r_0))^2,
//
// which is easily solvable quadratic equation in variable s. Using wxMaxima, we get following formula
// for our variable s:
//
// a.s^2 + b.s + c = 0,
//
// where:
//
// a = x_1 * x_1 - r_1 * r_1 + 2.0 * r_0 * r_1 - r_0 * r_0 = (x_1 - r_1 + r_0) * (x_1 + r_1 - r_0)
// b = 2.0 * (-x_1 * x_p - r_0 * r_1 + r_0 * r_0)
// c = y_p * y_p + x_p * x_p - r_0 * r_0
//
Q_ASSERT(qIsNull(m_xStart));
const PDFReal x_p = mappedPoint.x();
const PDFReal y_p = mappedPoint.y();
const PDFReal x_1 = m_xEnd;
const PDFReal r_0 = m_r0;
const PDFReal r_1 = m_r1;
const PDFReal a = (x_1 - r_1 + r_0) * (x_1 + r_1 - r_0);
const PDFReal b = 2.0 * (-x_1 * x_p - r_0 * r_1 + r_0 * r_0);
const PDFReal c = y_p * y_p + x_p * x_p - r_0 * r_0;
const PDFReal Dsqr = b * b - 4.0 * a * c;
if (Dsqr < 0.0)
{
return false;
}
const PDFReal D = std::sqrt(Dsqr);
PDFReal s1 = (-b - D) / (2.0 * a);
PDFReal s2 = (-b + D) / (2.0 * a);
PDFReal s = 0.0;
if (s1 < 0.0 && m_radialShadingPattern->isExtendStart())
{
s1 = 0.0;
}
if (s2 > 1.0 && m_radialShadingPattern->isExtendEnd())
{
s2 = 1.0;
}
const bool s1Valid = s1 >= 0.0 && s1 <= 0.0;
const bool s2Valid = s2 >= 0.0 && s2 <= 0.0;
if (s2Valid)
{
s = s2;
}
else if (s1Valid)
{
s = s1;
}
else
{
return false;
}
PDFReal t = interpolate(s, m_xStart, m_xEnd, m_tAtStart, m_tAtEnd);
t = qBound(m_tMin, t, m_tMax);
const auto& functions = m_radialShadingPattern->getFunctions();
std::array<PDFReal, PDF_MAX_COLOR_COMPONENTS> colorBuffer = { };
if (colorBuffer.size() < outputBuffer.size())
{
// Jakub Melka: Too much colors - we cant process it
return false;
}
if (functions.size() == 1)
{
Q_ASSERT(outputBuffer.size() <= colorBuffer.size());
PDFFunction::FunctionResult result = functions.front()->apply(&t, &t + 1, colorBuffer.data(), colorBuffer.data() + outputBuffer.size());
if (!result)
{
// Function call failed
return false;
}
}
else
{
if (functions.size() != outputBuffer.size())
{
// Invalid number of functions
return false;
}
Q_ASSERT(outputBuffer.size() <= colorBuffer.size());
for (size_t i = 0, count = outputBuffer.size(); i < count; ++i)
{
PDFFunction::FunctionResult result = functions[i]->apply(&t, &t + 1, colorBuffer.data() + i, colorBuffer.data() + i + 1);
if (!result)
{
// Function call failed
return false;
}
}
}
for (size_t i = 0, count = outputBuffer.size(); i < count; ++i)
{
outputBuffer[i] = colorBuffer[i];
}
return true;
}
private:
const PDFRadialShading* m_radialShadingPattern;
QMatrix m_p1p2GCS;
PDFReal m_xStart;
PDFReal m_xEnd;
PDFReal m_tAtStart;
PDFReal m_tAtEnd;
PDFReal m_tMin;
PDFReal m_tMax;
PDFReal m_r0;
PDFReal m_r1;
};
PDFShadingSampler* PDFRadialShading::createSampler(QMatrix userSpaceToDeviceSpaceMatrix) const
{
return new PDFRadialShadingSampler(this, userSpaceToDeviceSpaceMatrix);
}
ShadingType PDFFreeFormGouradTriangleShading::getShadingType() const
{
return ShadingType::FreeFormGouradTriangle;

4
Pdf4QtLib/sources/pdfpattern.h
View File

@@ -417,6 +417,10 @@ public:
virtual ShadingType getShadingType() const override;
virtual PDFMesh createMesh(const PDFMeshQualitySettings& settings, const PDFCMS* cms, RenderingIntent intent, PDFRenderErrorReporter* reporter) const override;
virtual PDFShadingSampler* createSampler(QMatrix userSpaceToDeviceSpaceMatrix) const override;
PDFReal getR0() const { return m_r0; }
PDFReal getR1() const { return m_r1; }
private:
friend class PDFPattern;