void Interpolator2D::CalculateGrid ( )

inlineprivate

the weights used for the interpolation

Calculate the collection of circles/triangles which describe the input grid. This is the collection of circles which are calculated from any three points and do not contain any other point of the grid.

Definition at line 90 of file Interpolator2D.h.

References Interpolator2D::vec::dist(), Interpolator2D::circle::isInsideCircle(), Interpolator2D::vec::orto(), Interpolator2D::circle::p, Interpolator2D::circle::r, Interpolator2D::vec::x, and Interpolator2D::vec::y.

Referenced by SetInputGrid().

    {
        circles.reserve(2*inputGrid.size());

        // Loop over all triplets of points
        for (auto it0=inputGrid.cbegin(); it0<inputGrid.cend(); it0++)
        {
            for (auto it1=inputGrid.cbegin(); it1<it0; it1++)
            {
                for (auto it2=inputGrid.cbegin(); it2<it1; it2++)
                {
                    // Calculate the circle through the three points

                    // Vectors along the side of the corresponding triangle
                    const vec v1 = *it1 - *it0;
                    const vec v2 = *it2 - *it1;

                    // Orthogonal vectors on the sides
                    const vec n1 = v1.orto();
                    const vec n2 = v2.orto();

                    // Center point of two of the three sides
                    const vec p1 = (*it0 + *it1)/2;
                    const vec p2 = (*it1 + *it2)/2;

                    // Calculate the crossing point of the two
                    // orthogonal vectors originating in the
                    // center of the sides.
                    const double denom = n1^n2;
                    if (denom==0)
                        continue;

                    const vec x(n1.x, n2.x);
                    const vec y(n1.y, n2.y);

                    const vec w(p1^(p1+n1), p2^(p2+n2));

                    circle c;

                    // This is the x and y coordinate of the circle
                    // through the three points and the circle's radius.
                    c.x = (x^w)/denom;
                    c.y = (y^w)/denom;
                    c.r = c.dist(*it1);

                    // Check if any other grid point lays within this circle
                    auto it3 = inputGrid.cbegin();
                    for (; it3<inputGrid.cend(); it3++)
                    {
                        if (it3==it0 || it3==it1 || it3==it2)
                            continue;

                        if (c.isInsideCircle(*it3))
                            break;
                    }

                    // If a point was found inside, reject the circle
                    if (it3!=inputGrid.cend())
                        continue;

                    // Store the three points of the triangle
                    c.p[0] = *it0;
                    c.p[1] = *it1;
                    c.p[2] = *it2;

                    // Keep in list
                    circles.push_back(c);
                }
            }
        }
    }

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