// -------------------------------------------------------------------------------------------------------------------- // // http://oxyplot.codeplex.com, license: Ms-PL // // -------------------------------------------------------------------------------------------------------------------- namespace OxyPlot { using System; /// /// Conrec is a straightforward method of contouring some surface represented /// as a regular triangular mesh. /// /// /// /// Ported from C / Fortran code by Paul Borke. /// See for /// for full description of code and the original source. /// /// /// Contouring aids in visualizing three dimensional surfaces on a two dimensional /// medium (on paper or in this case a computer graphics screen). Two most common /// applications are displaying topological features of an area on a map or the air /// pressure on a weather map. In all cases some parameter is plotted as a function /// of two variables, the longitude and latitude or x and y axis. One problem with /// computer contouring is the process is usually CPU intensive and the algorithms /// often use advanced mathematical techniques making them susceptible to error. /// /// public class Conrec { #region Delegates /// /// Renderer delegate /// /// /// Start point x-coordinate /// /// /// Start point y-coordinate /// /// /// End point x-coordinate /// /// /// End point y-coordinate /// /// /// Contour level /// public delegate void RendererDelegate(double x1, double y1, double x2, double y2, double z); #endregion #region Public Methods /// /// Contour is a contouring subroutine for rectangularily spaced data /// It emits calls to a line drawing subroutine supplied by the user /// which draws a contour map corresponding to data on a randomly /// spaced rectangular grid. The coordinates emitted are in the same /// units given in the x() and y() arrays. /// Any number of contour levels may be specified but they must be /// in order of increasing value. /// /// /// Matrix of data to contour. /// /// /// Data matrix column coordinates. /// /// /// Data matrix row coordinates. /// /// /// Contour levels in increasing order. /// /// /// The renderer. /// public static void Contour(double[,] d, double[] x, double[] y, double[] z, RendererDelegate renderer) { double x1 = 0.0; double x2 = 0.0; double y1 = 0.0; double y2 = 0.0; var h = new double; var sh = new int; var xh = new double; var yh = new double; int ilb = d.GetLowerBound(0); int iub = d.GetUpperBound(0); int jlb = d.GetLowerBound(1); int jub = d.GetUpperBound(1); int nc = z.Length; // The indexing of im and jm should be noted as it has to start from zero // unlike the fortran counter part int[] im = { 0, 1, 1, 0 }; int[] jm = { 0, 0, 1, 1 }; // Note that castab is arranged differently from the FORTRAN code because // Fortran and C/C++ arrays are transposed of each other, in this case // it is more tricky as castab is in 3 dimension int[,,] castab = { { { 0, 0, 8 }, { 0, 2, 5 }, { 7, 6, 9 } }, { { 0, 3, 4 }, { 1, 3, 1 }, { 4, 3, 0 } }, { { 9, 6, 7 }, { 5, 2, 0 }, { 8, 0, 0 } } }; Func xsect = (p1, p2) => (h[p2] * xh[p1] - h[p1] * xh[p2]) / (h[p2] - h[p1]); Func ysect = (p1, p2) => (h[p2] * yh[p1] - h[p1] * yh[p2]) / (h[p2] - h[p1]); for (int j = jub - 1; j >= jlb; j--) { int i; for (i = ilb; i <= iub - 1; i++) { double temp1 = Math.Min(d[i, j], d[i, j + 1]); double temp2 = Math.Min(d[i + 1, j], d[i + 1, j + 1]); double dmin = Math.Min(temp1, temp2); temp1 = Math.Max(d[i, j], d[i, j + 1]); temp2 = Math.Max(d[i + 1, j], d[i + 1, j + 1]); double dmax = Math.Max(temp1, temp2); if (dmax >= z && dmin <= z[nc - 1]) { int k; for (k = 0; k < nc; k++) { if (z[k] >= dmin && z[k] <= dmax) { int m; for (m = 4; m >= 0; m--) { if (m > 0) { // The indexing of im and jm should be noted as it has to // start from zero h[m] = d[i + im[m - 1], j + jm[m - 1]] - z[k]; xh[m] = x[i + im[m - 1]]; yh[m] = y[j + jm[m - 1]]; } else { h = 0.25 * (h + h + h + h); xh = 0.5 * (x[i] + x[i + 1]); yh = 0.5 * (y[j] + y[j + 1]); } if (h[m] > 0.0) { sh[m] = 1; } else if (h[m] < 0.0) { sh[m] = -1; } else { sh[m] = 0; } } // Note: at this stage the relative heights of the corners and the // centre are in the h array, and the corresponding coordinates are // in the xh and yh arrays. The centre of the box is indexed by 0 // and the 4 corners by 1 to 4 as shown below. // Each triangle is then indexed by the parameter m, and the 3 // vertices of each triangle are indexed by parameters m1,m2,and // m3. // It is assumed that the centre of the box is always vertex 2 // though this isimportant only when all 3 vertices lie exactly on // the same contour level, in which case only the side of the box // is drawn. // vertex 4 +-------------------+ vertex 3 // | \ / | // | \ m-3 / | // | \ / | // | \ / | // | m=2 X m=2 | the centre is vertex 0 // | / \ | // | / \ | // | / m=1 \ | // | / \ | // vertex 1 +-------------------+ vertex 2 // Scan each triangle in the box for (m = 1; m <= 4; m++) { int m1 = m; int m2 = 0; int m3; if (m != 4) { m3 = m + 1; } else { m3 = 1; } int caseValue = castab[sh[m1] + 1, sh[m2] + 1, sh[m3] + 1]; if (caseValue != 0) { switch (caseValue) { case 1: // Line between vertices 1 and 2 x1 = xh[m1]; y1 = yh[m1]; x2 = xh[m2]; y2 = yh[m2]; break; case 2: // Line between vertices 2 and 3 x1 = xh[m2]; y1 = yh[m2]; x2 = xh[m3]; y2 = yh[m3]; break; case 3: // Line between vertices 3 and 1 x1 = xh[m3]; y1 = yh[m3]; x2 = xh[m1]; y2 = yh[m1]; break; case 4: // Line between vertex 1 and side 2-3 x1 = xh[m1]; y1 = yh[m1]; x2 = xsect(m2, m3); y2 = ysect(m2, m3); break; case 5: // Line between vertex 2 and side 3-1 x1 = xh[m2]; y1 = yh[m2]; x2 = xsect(m3, m1); y2 = ysect(m3, m1); break; case 6: // Line between vertex 3 and side 1-2 x1 = xh[m3]; y1 = yh[m3]; x2 = xsect(m1, m2); y2 = ysect(m1, m2); break; case 7: // Line between sides 1-2 and 2-3 x1 = xsect(m1, m2); y1 = ysect(m1, m2); x2 = xsect(m2, m3); y2 = ysect(m2, m3); break; case 8: // Line between sides 2-3 and 3-1 x1 = xsect(m2, m3); y1 = ysect(m2, m3); x2 = xsect(m3, m1); y2 = ysect(m3, m1); break; case 9: // Line between sides 3-1 and 1-2 x1 = xsect(m3, m1); y1 = ysect(m3, m1); x2 = xsect(m1, m2); y2 = ysect(m1, m2); break; default: break; } renderer(x1, y1, x2, y2, z[k]); } } } } } } } } #endregion } }