From 01eea90b3cbadb30099ad09226e14eeb00841927 Mon Sep 17 00:00:00 2001 From: Irlan <-> Date: Tue, 17 Apr 2018 02:29:37 -0300 Subject: [PATCH] typos --- src/bounce/dynamics/shapes/hull_shape.cpp | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/src/bounce/dynamics/shapes/hull_shape.cpp b/src/bounce/dynamics/shapes/hull_shape.cpp index d5f1165..96ddcb5 100644 --- a/src/bounce/dynamics/shapes/hull_shape.cpp +++ b/src/bounce/dynamics/shapes/hull_shape.cpp @@ -90,28 +90,27 @@ void b3HullShape::ComputeMass(b3MassData* data, float32 density) const // int(f(x, y, z) * dV) = sum(int(dot(F, N_k) * dS)), k..n. // If the normal N_k is constant over the triangle and s is an axis in the direction of F, // we can bring N_k outside the integral - // int(dV) = sum(dot(N_k, s) * int(f(x, y, z) * dS)), k..n. + // int(f(x, y, z) * dV) = sum(dot(N_k, s) * int(g(x, y, z) * dS)), k..n. - // We need to compute surface integrals, where the f above is to be integrated along a triangle. + // We need to compute surface integrals, where the g above is to be integrated along a triangle. // Changing coordinates from (x, y, z) to (u, v) a formula for a integral along the triangle is - // int(f(x(u, v), y(u, v), z(u, v)) * norm(cross(e1, e2)) * du * dv) - // where f is a parametrization for a triangle + // int(g(x(u, v), y(u, v), z(u, v)) * norm(cross(e1, e2)) * du * dv) + // where g is a parametrization for a triangle // x = x1 + e1x * u + e2x * v // y = y1 + e1y * u + e2y * v // z = z1 + e1z * u + e2z * v // and 0 <= u, 0 <= v, u + v <= 1 // We can view the surface integral above also as - // int(f * det(D) * du * dv) + // int(g * det(D) * du * dv) // where D is the Jacobian of the parametrization: // D = cross(e1, e2) - + // We integrate x, y, and z over [0, 1 - v] and then over [0, 1]. + // Thus, using the fact that // N_k = D / norm(D), // the surface integral can be further simplified to - // sum(dot(D, s) * int(f(x(u, v), y(u, v), z(u, v)) * du * dv)) + // sum(dot(D, s) * int(g(x(u, v), y(u, v), z(u, v)) * du * dv)) - // We integrate f over [0, 1 - v] and then over [0, 1]. - // These double integrals are done either by a CAS or by hand. // Here, it was used the great SymPy. // SymPy was available at http://live.sympy.org/