Function _generate_normals

lib/mpl_toolkits/mplot3d/art3d.py:1678–1719

Compute the normals of a list of polygons, one normal per polygon. Normals point towards the viewer for a face with its vertices in counterclockwise order, following the right hand rule. Uses three points equally spaced around the polygon. This method assumes that the points a

(polygons)

def _generate_normals(polygons):
    """
    Compute the normals of a list of polygons, one normal per polygon.

    Normals point towards the viewer for a face with its vertices in
    counterclockwise order, following the right hand rule.

    Uses three points equally spaced around the polygon. This method assumes
    that the points are in a plane. Otherwise, more than one shade is required,
    which is not supported.

    Parameters
    ----------
    polygons : list of (M_i, 3) array-like, or (..., M, 3) array-like
        A sequence of polygons to compute normals for, which can have
        varying numbers of vertices. If the polygons all have the same
        number of vertices and array is passed, then the operation will
        be vectorized.

    Returns
    -------
    normals : (..., 3) array
        A normal vector estimated for the polygon.
    """
    if isinstance(polygons, np.ndarray):
        # optimization: polygons all have the same number of points, so can
        # vectorize
        n = polygons.shape[-2]
        i1, i2, i3 = 0, n//3, 2*n//3
        v1 = polygons[..., i1, :] - polygons[..., i2, :]
        v2 = polygons[..., i2, :] - polygons[..., i3, :]
    else:
        # The subtraction doesn't vectorize because polygons is jagged.
        v1 = np.empty((len(polygons), 3))
        v2 = np.empty((len(polygons), 3))
        for poly_i, ps in enumerate(polygons):
            n = len(ps)
            ps = np.asarray(ps)
            i1, i2, i3 = 0, n//3, 2*n//3
            v1[poly_i, :] = ps[i1, :] - ps[i2, :]
            v2[poly_i, :] = ps[i2, :] - ps[i3, :]
    return np.cross(v1, v2)


def _shade_colors(color, normals, lightsource=None):