Rigid body parameters of closed surface meshes

Fast computation of exact rigid body parameters of closed triangular surface meshes using divergence theorem

Rigid Body Parameters

In order to simulate dynamic behaviour of a rigid-body, one requires knowledge of a set of rigid-body parameters such as the total mass of the rigid-body, the center of mass, as well as the moments and products of inertia. The purpose of this submission is to provide a function which computes exact rigid-body parameters of objects represented by closed, triangular surface meshes. The principles underlying the calculations are based on the divergence theorem and are explained in detail in the attached .pdf document. This submission also includes two functions that take as input an arbitrary mesh and output parameters of a primitive object, such as an ellipsoid or a cuboid, with exactly the same inertial parameters as the input object. Finally, VisualizeLocaFrame.m function can be used for visualizing local frames of reference constructed from principal axes of inertia.

Quick Demo

load('sample_mesh') 	
RBP=RigidBodyParams(TR);
disp(RBP)
VisualizeLocalFrame(TR)

Enforcing Consistent and Proper Face Orientation

All calculations are based on the assumption that the input mesh is closed, manifold, and has outward pointing normals. To obtain outward point normals, the vertices of all faces must have counterclockwise ordering. If you know or suspect the input the mesh has either inconsistent or improper face orientation use function ConsistentNormalOrientation prior to computing the rigid-body parameters. Here is an example:

load('sample_mesh')
[F,V]=GetMeshData(TR);

% Randomly mix-up orientations of the faces to simulate the problem above
Nf=size(F,1);
idx=randn(Nf,1)>0;	
F2=F;
F2(idx,:)=fliplr(F(idx,:));
TR2=triangulation(F2,V);
fprintf('\nNumber of inverted faces: %d\n',nnz(idx))
	
% Enforce proper face orientation
[TR2_fix,cnt]=ConsistentNormalOrientation(TR2);
fprintf('Number of faces corrected: %d\n\n',cnt)

% Verify that the output is identical to RBP for the original mesh
RBP_fix=RigidBodyParams(TR2_fix);

fprintf('Corrected mesh:\n')
disp(RBP_fix)

fprintf('Original (reference) mesh:\n')
disp(RigidBodyParams(TR))

% Result you would have gotten without ensuring proper face orientation:
RBP2=RigidBodyParams(TR2);
fprintf('Uncorrected mesh:\n')
disp(RBP2)

License

MIT © 2019 Anton Semechko [e-mail]