Constructing curved structures like circles, ellipses, domes, and spheres in block-based sandbox games (like Minecraft) is challenging because the game world is composed of discrete, cubic voxels. To build a curved structure, you must translate smooth, continuous mathematical curves into a grid of squares, a process known as voxel rasterization.
Our tool utilizes Bresenham's circle algorithm and distance-based checks to select the optimal coordinates. For any cell (X, Y) in the grid, the algorithm calculates its distance from the circle's center. If the distance is close to the target radius (within a ±0.5 block margin), the voxel is highlighted as a shell block. For even-diameter shapes, the center point falls between four blocks, whereas for odd-diameter shapes, the center rests directly on a single block, altering the layout symmetry.
A sphere is rendered by slicing it horizontally into layers. At each layer index, the tool calculates the height offset from the sphere's equator and applies the Pythagorean theorem (r_layer = sqrt(r_sphere2 - height2)) to find the horizontal circle radius for that layer. You can navigate these layers one-by-one to build complex domes and spheres block-by-block.
Bresenham's circle algorithm is a mathematical method used in computer graphics to determine the pixels or grid blocks needed to draw a close approximation of a circle. It uses fast integer arithmetic to select the closest grid cells to the actual circle path.
A sphere is built by stack horizontal layers of varying circles on top of each other. A dome is simply the top half of a sphere. Use our layer navigator to see the exact block arrangement for each horizontal slice, building from the ground up.
Odd-diameter circles have a single central block, resulting in a symmetrical layout with clear cardinal lines. Even-diameter circles have their center point at the intersection of four blocks, requiring a 2x2 central grid and altering the curvature angles.