Twisted Drop

pinshape

Summary This is a mathematical doodle created with my marching cubes code. It's an isosurface of squashed and rotated spheres that change as you move up the model. Print Settings Printer: Eaglemoss Vector3 Rafts: Yes Supports: Yes Resolution: 0.2 mm Infill: 20% The bottom is quite curved, with several overhangs, so a raft and supports are required for this model. How I Designed This I started by using code I give my students to help them begin 3D graphics projects. This code helps them create models programmatically in Vertex and Index Buffers. I then used the Marching Cubes function to feed an equation into the code, which produced a Vertex Buffer containing the given isosurface of that equation. The model was created in a cubic region with sides measuring 2 Pi, centered at the origin, and using a 100 x 100 x 100 grid of values. Value Function This is the code used to calculate the function/equation value for a given point in space: float VBMarchCubes::function(Vector3 _pos) { _pos *= 2.0; float w = _pos.z *1.2f; float x = (_pos.x *cos(w) - _pos.y * sin(w))/(0.25*(_pos.z+XM_PI)), y = (_pos.x*sin(w)+_pos.y*cos(w)) /(0.25* (_pos.z + XM_PI)), z = _pos.z; float x1 = _pos.x, y1 = _pos.y, z1 = _pos.z; return ((x + 1)*(x + 1) + (y + 1)*(y + 1) + (z -2)*(z -2) - XM_PIDIV2*XM_PIDIV2)*((x - 1)*(x - 1) + (y - 1)*(y - 1) + (z -2)*(z -2) - XM_PIDIV2*XM_PIDIV2) *((x - 1)*(x - 1) + (y + 1)*(y + 1) + (z - 1)*(z - 1) - XM_PIDIV2*XM_PIDIV2)*((x + 1)*(x + 1) + (y - 1)*(y - 1) + (z - 1)*(z - 1) - XM_PIDIV2*XM_PIDIV2) *( (x + 1)*(x + 1) + (y + 1)*(y + 1) + (z + 1)*(z + 1) - XM_PIDIV2*XM_PIDIV2)*((x - 1)*(x - 1) + (y - 1)*(y - 1) + (z + 1)*(z + 1) - XM_PIDIV2*XM_PIDIV2) *((x1*x1/(XM_PI*XM_PI)+y1*y1/(XM_PI*XM_PI)+(z1-4)*(z1-4)/(XM_PIDIV4*XM_PIDIV4))-1); }