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@@ -0,0 +1,256 @@
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+ /**************************************\
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+ * *
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+ * OpenSCAD Mesh Display *
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+ * by Thinkyhead - April 2017 *
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+ * *
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+ * Copy the grid output from Marlin, *
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+ * paste below as shown, and use *
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+ * OpenSCAD to see a visualization *
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+ * of your mesh. *
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+ * *
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+ \**************************************/
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+
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+//$t = 0.15; // comment out during animation
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+
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+//
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+// Mesh info and points
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+//
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+
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+mesh_width = 200; // X Size in mm of the probed area
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+mesh_height = 200; // Y Size...
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+zprobe_offset = 0; // Added to the points
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+NAN = 0; // Z to use for un-measured points
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+
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+measured_z = [
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+ [ -1.20, -1.13, -1.09, -1.03, -1.19 ],
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+ [ -1.16, -1.25, -1.27, -1.25, -1.08 ],
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+ [ -1.13, -1.26, -1.39, -1.31, -1.18 ],
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+ [ -1.09, -1.20, -1.26, -1.21, -1.18 ],
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+ [ -1.13, -0.99, -1.03, -1.06, -1.32 ]
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+];
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+
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+//
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+// Geometry
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+//
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+
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+max_z_scale = 100; // Scale at Time 0.5
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+min_z_scale = 10; // Scale at Time 0.0 and 1.0
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+thickness = 0.5; // thickness of the mesh triangles
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+tesselation = 1; // levels of tesselation from 0-2
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+alternation = 2; // direction change modulus (try it)
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+
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+//
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+// Appearance
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+//
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+
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+show_plane = true;
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+show_labels = true;
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+arrow_length = 5;
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+
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+label_font_lg = "Arial";
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+label_font_sm = "Arial";
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+mesh_color = [1,1,1,0.5];
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+plane_color = [0.4,0.6,0.9,0.6];
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+
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+//================================================ Derive useful values
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+
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+big_z = max_2D(measured_z,0);
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+lil_z = min_2D(measured_z,0);
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+
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+mean_value = (big_z + lil_z) / 2.0;
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+
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+mesh_points_y = len(measured_z);
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+mesh_points_x = len(measured_z[0]);
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+
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+xspace = mesh_width / (mesh_points_x - 1);
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+yspace = mesh_height / (mesh_points_y - 1);
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+
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+// At $t=0 and $t=1 scale will be 100%
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+z_scale_factor = min_z_scale + (($t > 0.5) ? 1.0 - $t : $t) * (max_z_scale - min_z_scale) * 2;
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+
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+//
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+// Min and max recursive functions for 1D and 2D arrays
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+// Return the smallest or largest value in the array
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+//
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+function min_1D(b,i) = (i<len(b)-1) ? min(b[i], min_1D(b,i+1)) : b[i];
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+function min_2D(a,j) = (j<len(a)-1) ? min_2D(a,j+1) : min_1D(a[j], 0);
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+function max_1D(b,i) = (i<len(b)-1) ? max(b[i], max_1D(b,i+1)) : b[i];
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+function max_2D(a,j) = (j<len(a)-1) ? max_2D(a,j+1) : max_1D(a[j], 0);
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+
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+//
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+// Get the corner probe points of a grid square.
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+//
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+// Input : x,y grid indexes
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+// Output : An array of the 4 corner points
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+//
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+function grid_square(x,y) = [
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+ [x * xspace, y * yspace, z_scale_factor * (measured_z[y][x] - mean_value)],
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+ [x * xspace, (y+1) * yspace, z_scale_factor * (measured_z[y+1][x] - mean_value)],
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+ [(x+1) * xspace, (y+1) * yspace, z_scale_factor * (measured_z[y+1][x+1] - mean_value)],
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+ [(x+1) * xspace, y * yspace, z_scale_factor * (measured_z[y][x+1] - mean_value)]
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+];
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+
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+// The corner point of a grid square with Z centered on the mean
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+function pos(x,y,z) = [x * xspace, y * yspace, z_scale_factor * (z - mean_value)];
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+
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+//
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+// Draw the point markers and labels
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+//
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+module point_markers(show_home=true) {
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+ // Mark the home position 0,0
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+ color([0,0,0,0.25]) translate([1,1]) cylinder(r=1, h=z_scale_factor, center=true);
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+
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+ for (x=[0:mesh_points_x-1], y=[0:mesh_points_y-1]) {
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+ z = measured_z[y][x];
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+ down = z < mean_value;
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+ translate(pos(x, y, z)) {
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+
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+ // Label each point with the Z
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+ if (show_labels) {
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+ v = z - mean_value;
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+
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+ color(abs(v) < 0.1 ? [0,0.5,0] : [0.25,0,0])
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+ translate([0,0,down?-10:10]) {
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+
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+ $fn=8;
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+ rotate([90,0])
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+ text(str(z), 6, label_font_lg, halign="center", valign="center");
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+
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+ translate([0,0,down?-6:6]) rotate([90,0])
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+ text(str(down ? "" : "+", v), 3, label_font_sm, halign="center", valign="center");
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+ }
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+ }
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+
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+ // Show an arrow pointing up or down
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+ rotate([0, down ? 180 : 0]) translate([0,0,-1])
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+ cylinder(
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+ r1=0.5,
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+ r2=0.1,
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+ h=arrow_length, $fn=12, center=1
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+ );
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+ }
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+ }
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+}
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+
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+//
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+// Split a square on the diagonal into
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+// two triangles and render them.
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+//
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+// s : a square
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+// alt : a flag to split on the other diagonal
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+//
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+module tesselated_square(s, alt=false) {
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+ add = [0,0,thickness];
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+ p1 = [
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+ s[0], s[1], s[2], s[3],
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+ s[0]+add, s[1]+add, s[2]+add, s[3]+add
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+ ];
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+ f1 = alt
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+ ? [ [0,1,3], [4,5,1,0], [4,7,5], [5,7,3,1], [7,4,0,3] ]
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+ : [ [0,1,2], [4,5,1,0], [4,6,5], [5,6,2,1], [6,4,0,2] ];
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+ f2 = alt
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+ ? [ [1,2,3], [5,6,2,1], [5,6,7], [6,7,3,2], [7,5,1,3] ]
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+ : [ [0,2,3], [4,6,2,0], [4,7,6], [6,7,3,2], [7,4,0,3] ];
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+
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+ // Use the other diagonal
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+ polyhedron(points=p1, faces=f1);
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+ polyhedron(points=p1, faces=f2);
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+}
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+
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+/**
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+ * The simplest mesh display
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+ */
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+module simple_mesh(show_plane=show_plane) {
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+ if (show_plane) color(plane_color) cube([mesh_width, mesh_height, thickness]);
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+ color(mesh_color)
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+ for (x=[0:mesh_points_x-2], y=[0:mesh_points_y-2])
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+ tesselated_square(grid_square(x, y));
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+}
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+
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+/**
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+ * Subdivide the mesh into smaller squares.
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+ */
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+module bilinear_mesh(show_plane=show_plane,tesselation=tesselation) {
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+ if (show_plane) color(plane_color) translate([-5,-5]) cube([mesh_width+10, mesh_height+10, thickness]);
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+ tesselation = tesselation % 4;
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+ color(mesh_color)
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+ for (x=[0:mesh_points_x-2], y=[0:mesh_points_y-2]) {
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+ square = grid_square(x, y);
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+ if (tesselation < 1) {
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+ tesselated_square(square,(x%alternation)-(y%alternation));
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+ }
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+ else {
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+ subdiv_4 = subdivided_square(square);
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+ if (tesselation < 2) {
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+ for (i=[0:3]) tesselated_square(subdiv_4[i],i%alternation);
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+ }
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+ else {
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+ for (i=[0:3]) {
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+ subdiv_16 = subdivided_square(subdiv_4[i]);
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+ if (tesselation < 3) {
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+ for (j=[0:3]) tesselated_square(subdiv_16[j],j%alternation);
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+ }
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+ else {
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+ for (j=[0:3]) {
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+ subdiv_64 = subdivided_square(subdiv_16[j]);
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+ if (tesselation < 4) {
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+ for (k=[0:3]) tesselated_square(subdiv_64[k]);
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+ }
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+ }
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+ }
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+ }
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+ }
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+ }
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+
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+ }
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+}
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+
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+//
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+// Subdivision helpers
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+//
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+function ctrz(a) = (a[0][2]+a[1][2]+a[3][2]+a[2][2])/4;
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+function avgx(a,i) = (a[i][0]+a[(i+1)%4][0])/2;
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+function avgy(a,i) = (a[i][1]+a[(i+1)%4][1])/2;
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+function avgz(a,i) = (a[i][2]+a[(i+1)%4][2])/2;
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+
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+//
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+// Convert one square into 4, applying bilinear averaging
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+//
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+// Input : 1 square (4 points)
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+// Output : An array of 4 squares
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+//
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+function subdivided_square(a) = [
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+ [ // SW square
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+ a[0], // SW
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+ [a[0][0],avgy(a,0),avgz(a,0)], // CW
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+ [avgx(a,1),avgy(a,0),ctrz(a)], // CC
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+ [avgx(a,1),a[0][1],avgz(a,3)] // SC
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+ ],
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+ [ // NW square
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+ [a[0][0],avgy(a,0),avgz(a,0)], // CW
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+ a[1], // NW
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+ [avgx(a,1),a[1][1],avgz(a,1)], // NC
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+ [avgx(a,1),avgy(a,0),ctrz(a)] // CC
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+ ],
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+ [ // NE square
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+ [avgx(a,1),avgy(a,0),ctrz(a)], // CC
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+ [avgx(a,1),a[1][1],avgz(a,1)], // NC
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+ a[2], // NE
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+ [a[2][0],avgy(a,0),avgz(a,2)] // CE
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+ ],
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+ [ // SE square
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+ [avgx(a,1),a[0][1],avgz(a,3)], // SC
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+ [avgx(a,1),avgy(a,0),ctrz(a)], // CC
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+ [a[2][0],avgy(a,0),avgz(a,2)], // CE
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+ a[3] // SE
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+ ]
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+];
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+
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+
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+//================================================ Run the plan
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+
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+translate([-mesh_width / 2, -mesh_height / 2]) {
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+ $fn = 12;
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+ point_markers();
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+ bilinear_mesh();
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+}
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Scott Lahteine