OrcaSlicer/docs/HLSD/center-of-mass.md

Center of mass markers — High Level Design

Purpose and scope

The "Center of mass" item of the canvas toolbar menu, in the bottom left corner of the 3D view, marks where the mass of the plate, of each object instance and of each body of an assembly is centered, in Prepare and in Preview. It helps judge how parts will rest on the plate, for instance whether a tall or leaning part could tip. It is a view setting: it changes nothing in the model, the slice or the project file, and it does not reach plate thumbnails. The choice is kept in the app config as show_center_of_mass, off by default. The assembly view and the Design tab have no markers.

Three kinds of marker share one shape, a sphere whose octants alternate between two colors:

• each plate, black and white, for everything on it;
• each object instance, light blue and white;
• each body of an assembly, red and yellow;
• in Preview, the supports and raft of each object instance, green and black.

A click on a marker opens a box beside it with the weight and volume of what it stands for, where its center lies in that thing's bounding box and the size of the box, and its moments of inertia about axes through the center parallel to x, y and z.

An assembly is an object of several parts or with negative volumes. Its bodies are the connected solids its parts make once united, the bodies the separated infills option centers its infill on (see separated-infills.md): parts that overlap or touch are one body, parts apart are separate bodies. An object of one body, and every object of a single part, has no body markers, as its object marker says it all.

Mass is volume times density, the filament_density of the filament that prints it, or 1.245 g/cm³ (DEFAULT_FILAMENT_DENSITY) for a filament without one. Prepare has the model only, so it takes each part as a solid of the density of its filament, the part's own or else its object's. It reads each filament's density from the filament's selected preset, edits not yet saved included, as slicing does: the plater's own config holds the values of the filament edited last only. Preview has what will be printed, so its markers come from the toolpaths, whose mass depends on walls, infill and flow as well. There the solid markers are for what is printed up to the top layer the layer slider shows: for the plate with brim, raft and supports, where the weight rests at that point of the print; for an object or a body, its own extrusions. Each has a faded twin for the same at the end of the print, so the slider shows the weight moving toward where it ends, and at the top layer the two meet. In Prepare the plate has the model alone, as brim, raft and supports exist only once sliced.

Prepare: from the meshes

An object of one part takes the mass properties of its mesh at unit density, times its density, from its_mass_properties(), which handles a mesh in a single pass. Each triangle and a fixed vertex of the mesh span a tetrahedron whose signed volume is V = a · (b × c) / 6, with a, b, c taken relative to that vertex. By the divergence theorem these volumes add up to the volume of a closed mesh, their volume-weighted centroids to its center of mass, and their second moments V (a aᵀ + b bᵀ + c cᵀ + s sᵀ) / 20, with s = a + b + c, to its own. Shells facing inward, such as a cavity, subtract themselves, and flipping every triangle changes nothing. The sums are kept in double precision and relative to a vertex of the mesh rather than the origin, which keeps them exact for meshes far from it. The result keeps the spread of the mass about its center, (x - c)(x - c)ᵀ averaged over the mass, from which the moments of inertia follow.

The CGAL routines that look alike do not compute this. CGAL::centroid weighs tetrahedra by their unsigned volume, so it fails on cavities and on any shell that is not star-shaped from the fan's apex; over triangles it returns the centroid of the surface, and over points the average of the vertices, which depends on the tessellation. CGAL::barycenter with the signed volumes as weights gives the same answer, but only after copying every tetrahedron into a vector of weighted points, and takes two and a half times as long.

A mesh's result is in its own coordinates. Each GLVolume maps it to the world with its world matrix M, and weighs it by the volume times the absolute determinant of that matrix: a center of mass moves with any affine map, and the spread becomes L S Lᵀ for the linear part L of M, so no mesh is ever transformed. The GLVolume's matrices, rather than the model's, let the markers follow an object while it is dragged, before the model is updated. Results are cached by ModelVolume id; a ModelVolume takes a new id whenever its mesh changes, which is the rule reload_scene() relies on to rebuild a GLVolume's geometry, so a cached result never outlives its mesh.

An assembly's parts overlap or touch, which the mesh formula would count twice, so solid_bodies() slices them instead, in the object's coordinates. It cuts the height into 500 slabs, 100 while a part is dragged, slices every part and negative volume at the middle of each slab, unites the parts and cuts the negative volumes away, and links the islands of neighboring slabs that overlap into bodies with connected_bodies(). Each island adds a prism of the slab's thickness at the density: its area, and its first and second moments of area, from the same sums over the outline as the area, with the slab's height for z. Where parts of different densities overlap, the later volume of the object counts, as slicing clips every part by the parts after it; each part then weighs the region it prints, which is credited to the island holding it. Each body also keeps the convex hull of its islands and the height they span, whose corners, once transformed, give its bounding box, tight while the instance turns about z only. The object is the sum of its bodies, its box that of its parts, as the object's size shows it, and each plate the sum of the object instances PartPlateList::find_instance() puts on it, so that an instance on no plate counts in none. The bodies are cached by ModelObject id with the volumes, types, densities and transformations they were sliced from.

Preview: from the toolpaths

GCodeProcessor sums the masses while it processes the G-code, in the same pass that builds the moves, and leaves them in GCodeProcessorResult; GCodeViewer keeps a copy of them when it loads a result. Nothing is stored per move.

Each extrusion weighs the volume of filament its E extrudes times the density of the filament that extrudes it, so a print of several materials weighs each as it is. Flow ratio, line widths, ironing and purging into infill all count as printed. Its mass spreads evenly along the segment the bead's center runs, half the layer height below the nozzle, in the frame of the stored moves: plate offset added, Z offset removed. Such a segment from a to b adds m (a + b) / 2 to the moments and m (a² + a b + b²) / 3 to the second moments along each axis, and its box widened by half the bead's height to the bounding box; not by half its width, which the processor only estimates, so that a box runs along the walls' center lines. Arcs are already split into segments by the processor. Walls, infill, top and bottom surfaces, ironing and gap fill make the parts. The brim and the support roles, the raft among them, count only in what the plate prints. The skirt, the prime tower and custom G-code count nowhere.

The plate takes every extrusion, so it needs nothing more. The objects and bodies need the sliced objects, which the G-code does not describe, so the G-code export hands the processor a locator built from the Print; G-code opened from a file, or from a project sliced earlier, has no Print behind it, and so shows the plate alone. Object labels would not do: profiles turn the four kinds Orca writes on and off in every combination, and none of them tells the bodies apart.

The locator numbers the object instances and, for each assembly, the bodies of every instance. It takes the bodies PrintObject::prepare_infill() found for separated infills, or, when that option did not need them, links the islands (Layer::lslices) of neighboring layers into bodies with the same connected_bodies(). For each extrusion of a part, it finds the first layer printed at or above its height, as spiral vase rises through each layer, and the island holding it with an IslandLocator, the one solid_bodies() credits its regions with: by the island's box, widened by 1 mm for walls reaching past it, with a polygon test only where boxes overlap, and the nearest outline where none holds the point. The boxes of one layer's islands say nothing of the other instances, so an instance whose widened box reaches another's, as copies placed side by side do, tests the outlines alone, and outside them the nearest outline of all such instances wins. The island gives both the instance and the body. The island found last is tried first, as extrusions mostly follow each other on one island. Brim, raft and supports lie outside the islands. The brim counts in the plate only; a support or raft extrusion goes to the instance whose footprint, the box of its widened islands, holds it, the one whose center is nearest among several, or else the nearest footprint, as supports stand below and around their object.

Each mass holds, for each layer id, the running total of what is printed up to that layer, the last of which is the faded marker's, so the solid marker for any slider position is a single lookup. The layer ids are those the moves carry, which are also the layers of libvgcode and of the slider; in a print by object they follow the order of printing, so the solid markers show the objects printed so far as they are.

Drawing

smooth_sphere() with a resolution divisible by four leaves every triangle within one octant, so it splits into two models drawn with the gouraud_light shader in each kind's two colors. The radius is 9 pixels for the plate, 7 for the objects, 6 for the supports and 5 for the bodies, scaled like the canvas toolbar for the display's DPI and kept constant on screen through the camera's inverse zoom. They are drawn in that order, so that markers at one place show as rings. The faded markers are the same spheres at 40% opacity, drawn before all the solid ones, which show over them where both meet.

The centers usually lie inside the objects, so the markers are drawn without the depth test and show through the objects and anything in front of them. Back face culling keeps the far half of a sphere from covering the near one. They are drawn after the ambient occlusion pass, which would otherwise darken them as the surface behind them, and before FXAA, which smooths their edges.

The markers are part of the cached scene, so toggling them, or changing a filament's density while they are shown, marks the scene dirty, and moving the layer slider redraws the scene with the solid markers where they belong. In Prepare they are hidden while any gizmo other than Move, Rotate, Scale and Lay on face is open, since the others work on the surface a marker would cover, and a hidden object has no markers.

Details

The markers drawn last are kept, and a left click is tested against them before it selects: each center and a point a radius to its right are projected to the screen, and the click hits a marker within that distance. The solid markers are tested before the faded ones and the smaller kinds before the larger, the order in which they cover each other. A hit opens the details of that marker and keeps the click from changing the selection; a click anywhere else closes them. The box is an ImGui window beside the marker, redrawn with the overlay from the markers of the last scene, so it follows a dragged object, and in Preview the layer slider. It closes when its marker is gone, or when the number of markers of its kind changes, as then it may stand for something else.

Its title says what the marker stands for: the plate, an object, an assembly or a part, the body of an assembly. The G-code export lists the object instances for the processor, marking assemblies, as it hands it the locator.

Each marker carries its sums: mass, volume, first moments and the second moments about the origin along each axis, Σ m x², Σ m y² and Σ m z², which add up from parts to objects to plates. The moment of inertia about the axis through the center parallel to x is then m (σy² + σz²), with σ² = Σ m x² / m - c² along each axis, and likewise for y and z. Masses are kept in mg, volume times density in g/cm³, and shown in g, volumes in cm³ and moments of inertia in g·mm². In Preview the box tells the finished print from what is printed up to the layer shown, the two weighing differently, and both are placed in the bounding box of everything the marker holds by the end.