sdf.py 文件源码

def curvature(self, coords, delta=0.001):
        """
        Returns an approximation to the local SDF curvature (Hessian) at the
        given coordinate in grid basis.

        Parameters
        ---------
        coords : numpy 3-vector
            the grid coordinates at which to get the curvature

        Returns
        -------
        curvature : 3x3 ndarray of the curvature at the surface points
        """
        # perturb local coords
        coords_x_up   = coords + np.array([delta, 0, 0])
        coords_x_down = coords + np.array([-delta, 0, 0])
        coords_y_up   = coords + np.array([0, delta, 0])
        coords_y_down = coords + np.array([0, -delta, 0])
        coords_z_up   = coords + np.array([0, 0, delta])
        coords_z_down = coords + np.array([0, 0, -delta])

        # get gradient
        grad_x_up = self.gradient(coords_x_up)
        grad_x_down = self.gradient(coords_x_down)
        grad_y_up = self.gradient(coords_y_up)
        grad_y_down = self.gradient(coords_y_down)
        grad_z_up = self.gradient(coords_z_up)
        grad_z_down = self.gradient(coords_z_down)

        # finite differences
        curvature_x = (grad_x_up - grad_x_down) / (4 * delta)
        curvature_y = (grad_y_up - grad_y_down) / (4 * delta)
        curvature_z = (grad_z_up - grad_z_down) / (4 * delta)
        curvature = np.c_[curvature_x, np.c_[curvature_y, curvature_z]]
        curvature = curvature + curvature.T
        return curvature