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[apps/calculation] additional_outputs: fix ellipsis equation in

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ComplexGraphView
This commit is contained in:
Émilie Feral
2020-01-09 13:47:56 +01:00
committed by Léa Saviot
parent c2364d27cd
commit 340bbb5644
1 changed files with 17 additions and 8 deletions
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25
apps/calculation/additional_outputs/complex_graph_cell.cpp
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@@ -21,7 +21,6 @@ void ComplexGraphView::drawRect(KDContext * ctx, KDRect rect) const {
float real = m_complex->real();
float imag = m_complex->imag();
float ph = std::arg(*m_complex);
/* Draw the segment from the origin to the dot (real, imag) of equation
* x(t) = t*real and y(t) = t*imag with t in [0,1] */
drawCurve(ctx, rect, 0.0f, 1.0f, 0.01f,
@@ -29,24 +28,34 @@ void ComplexGraphView::drawRect(KDContext * ctx, KDRect rect) const {
ComplexModel * complexModel = (ComplexModel *)model;
return Poincare::Coordinate2D<float>(complexModel->real()*t, complexModel->imag()*t);
}, m_complex, nullptr, false, Palette::GreyDark, false);
/* Draw the partial ellipse indicating the angle theta
/* Draw the partial ellipse indicating the angle θ
* - the ellipse parameters are a = |real|/5 and b = |imag|/5,
* - the parametric ellipse equation is x(t) = a*cos(θ*t) and y(t) = b*sin(θ*t)
* - the parametric ellipse equation is x(t) = a*cos(th*t) and y(t) = b*sin(th*t)
* with th computed in order to be the intersection of the line forming an
* angle θ with the abscissa and the ellipsis
* - we draw the ellipse for t in [0,1] to represent it from the abscissa axis
* to the phase of the complex
* to the phase of the complex
*/
/* Compute th: th is the intersection of ellipsis of equation (a*cos(t), b*sin(t))
* and the line of equation (t,t*tan(θ)).
* (a*cos(t), b*sin(t)) = (t,t*tan(θ)) --> t = arctan((a/b)*tan(θ)) (± π) */
float th = imag != 0.0f ? std::atan(std::fabs(real/imag)*std::tan(std::arg(*m_complex))) : 0.0f;
if (real < 0.0f) {
th += imag < 0.0f ? -M_PI : M_PI;
}
drawCurve(ctx, rect, 0.0f, 1.0f, 0.01f,
[](float t, void * model, void * context) {
ComplexModel * complexModel = (ComplexModel *)model;
float ph = *(float *)context;
float th = *(float *)context;
float factor = 5.0f;
float a = std::fabs(complexModel->real())/factor;
float b = std::fabs(complexModel->imag())/factor;
// Avoid flat ellipsis in edge cases (i or -i)
a = a == 0.0f ? 1.0f/factor : a;
b = b == 0.0f ? 1.0f/factor : b;
return Poincare::Coordinate2D<float>(a*std::cos(t*ph), b*std::sin(t*ph));
}, m_complex, &ph, false, Palette::GreyDark, false);
return Poincare::Coordinate2D<float>(a*std::cos(t*th), b*std::sin(t*th));
}, m_complex, &th, false, Palette::GreyDark, false);
// Draw dashed segment to indicate real and imaginary
drawSegment(ctx, rect, Axis::Vertical, real, 0.0f, imag, Palette::Red, 1, 3);
drawSegment(ctx, rect, Axis::Horizontal, imag, 0.0f, real, Palette::Red, 1, 3);
@@ -72,7 +81,7 @@ void ComplexGraphView::drawRect(KDContext * ctx, KDRect rect) const {
// we positioned its label consistently
real = real == 0.0f ? 1.0f : real;
imag = imag == 0.0f ? 1.0f : imag;
drawLabel(ctx, rect, std::fabs(real)/5.0f*std::cos(factor*ph), std::fabs(imag)/5.0f*std::sin(factor*ph), "arg(z)", Palette::Red, horizontalPosition, verticalPosition);
drawLabel(ctx, rect, std::fabs(real)/5.0f*std::cos(factor*th), std::fabs(imag)/5.0f*std::sin(factor*th), "arg(z)", Palette::Red, horizontalPosition, verticalPosition);
}
}