mesh-master/mesh/arcball.py

#!/usr/bin/env python
# encoding: utf-8
# Copyright (c) 2012 Max Planck Society. All rights reserved.

"""
Math utilities, vector, matrix types and ArcBall quaternion rotation class
==========================================================================

"""

import numpy as Numeric
import copy
from math import sqrt

# //assuming IEEE-754(GLfloat), which i believe has max precision of 7 bits
Epsilon = 1.0e-5


class ArcBallT(object):
    def __init__(self, NewWidth, NewHeight):
        self.m_StVec = Vector3fT()
        self.m_EnVec = Vector3fT()
        self.m_AdjustWidth = 1.0
        self.m_AdjustHeight = 1.0
        self.setBounds(NewWidth, NewHeight)

    def __str__(self):
        str_rep = ""
        str_rep += "StVec = " + str(self.m_StVec)
        str_rep += "\nEnVec = " + str(self.m_EnVec)
        str_rep += "\n scale coords %f %f" % (self.m_AdjustWidth, self.m_AdjustHeight)
        return str_rep

    def setBounds(self, NewWidth, NewHeight):
        # //Set new bounds
        assert (NewWidth > 1.0 and NewHeight > 1.0), "Invalid width or height for bounds."
        # //Set adjustment factor for width/height
        self.m_AdjustWidth = 1.0 / ((NewWidth - 1.0) * 0.5)
        self.m_AdjustHeight = 1.0 / ((NewHeight - 1.0) * 0.5)

    def _mapToSphere(self, NewPt):
        # Given a new window coordinate, will modify NewVec in place
        X = 0
        Y = 1
        Z = 2

        NewVec = Vector3fT()
        # //Copy paramter into temp point
        TempPt = copy.copy(NewPt)
        # //Adjust point coords and scale down to range of [-1 ... 1]
        TempPt[X] = (NewPt[X] * self.m_AdjustWidth) - 1.0
        TempPt[Y] = 1.0 - (NewPt[Y] * self.m_AdjustHeight)
        # //Compute the square of the length of the vector to the point from the center
        length = Numeric.sum(Numeric.dot(TempPt, TempPt))
        # //If the point is mapped outside of the sphere... (length > radius squared)
        if (length > 1.0):
            # //Compute a normalizing factor (radius / sqrt(length))
            norm = 1.0 / sqrt(length)

            # //Return the "normalized" vector, a point on the sphere
            NewVec[X] = TempPt[X] * norm
            NewVec[Y] = TempPt[Y] * norm
            NewVec[Z] = 0.0
        else:  # //Else it's on the inside
            # //Return a vector to a point mapped inside the sphere sqrt(radius squared - length)
            NewVec[X] = TempPt[X]
            NewVec[Y] = TempPt[Y]
            NewVec[Z] = sqrt(1.0 - length)

        return NewVec

    def click(self, NewPt):
        # Mouse down (Point2fT
        self.m_StVec = self._mapToSphere(NewPt)
        return

    def drag(self, NewPt):
        # Mouse drag, calculate rotation (Point2fT Quat4fT)
        """ drag (Point2fT mouse_coord) -> new_quaternion_rotation_vec
        """
        X = 0
        Y = 1
        Z = 2
        W = 3

        self.m_EnVec = self._mapToSphere(NewPt)

        # //Compute the vector perpendicular to the begin and end vectors
        # Perp = Vector3fT ()
        Perp = Vector3fCross(self.m_StVec, self.m_EnVec)

        NewRot = Quat4fT()
        # Compute the length of the perpendicular vector
        if (Vector3fLength(Perp) > Epsilon):
            # if its non-zero
            # We're ok, so return the perpendicular vector as the transform after all
            NewRot[X] = Perp[X]
            NewRot[Y] = Perp[Y]
            NewRot[Z] = Perp[Z]
            # //In the quaternion values, w is cosine (theta / 2), where theta is rotation angle
            NewRot[W] = Vector3fDot(self.m_StVec, self.m_EnVec)
        else:
            # if its zero
            # The begin and end vectors coincide, so return a quaternion of zero matrix (no rotation)
            NewRot[X] = NewRot[Y] = NewRot[Z] = NewRot[W] = 0.0

        return NewRot


def Matrix4fT():
    return Numeric.identity(4, 'f')


def Matrix3fT():
    return Numeric.identity(3, 'f')


def Quat4fT():
    return Numeric.zeros(4, 'f')


def Vector3fT():
    return Numeric.zeros(3, 'f')


def Point2fT(x=0.0, y=0.0):
    pt = Numeric.zeros(2, 'f')
    pt[0] = x
    pt[1] = y
    return pt


def Vector3fDot(u, v):
    # Dot product of two 3f vectors
    dotprod = Numeric.dot(u, v)
    return dotprod


def Vector3fCross(u, v):
    # Cross product of two 3f vectors
    X = 0
    Y = 1
    Z = 2
    cross = Numeric.zeros(3, 'f')
    cross[X] = (u[Y] * v[Z]) - (u[Z] * v[Y])
    cross[Y] = (u[Z] * v[X]) - (u[X] * v[Z])
    cross[Z] = (u[X] * v[Y]) - (u[Y] * v[X])
    return cross


def Vector3fLength(u):
    mag_squared = Numeric.sum(Numeric.dot(u, u))
    mag = sqrt(mag_squared)
    return mag


def Matrix3fSetIdentity():
    return Numeric.identity(3, 'f')


def Matrix3fMulMatrix3f(matrix_a, matrix_b):
    return matrix_a.dot(matrix_b)


def Matrix4fSVD(NewObj):
    X = 0
    Y = 1
    Z = 2
    s = sqrt(((NewObj[X][X] * NewObj[X][X]) + (NewObj[X][Y] * NewObj[X][Y]) + (NewObj[X][Z] * NewObj[X][Z]) +
              (NewObj[Y][X] * NewObj[Y][X]) + (NewObj[Y][Y] * NewObj[Y][Y]) + (NewObj[Y][Z] * NewObj[Y][Z]) +
              (NewObj[Z][X] * NewObj[Z][X]) + (NewObj[Z][Y] * NewObj[Z][Y]) + (NewObj[Z][Z] * NewObj[Z][Z])) / 3.0)
    return s


def Matrix4fSetRotationScaleFromMatrix3f(NewObj, three_by_three_matrix):
    """Modifies NewObj in-place by replacing its upper 3x3 portion from the
    passed in 3x3 matrix.

    :param NewObj: a `Matrix4fT`
    """
    NewObj[0:3, 0:3] = three_by_three_matrix
    return NewObj


def Matrix4fSetRotationFromMatrix3f(NewObj, three_by_three_matrix):
    """
    Sets the rotational component (upper 3x3) of this matrix to the matrix
    values in the T precision Matrix3d argument; the other elements of
    this matrix are unchanged; a singular value decomposition is performed
    on this object's upper 3x3 matrix to factor out the scale, then this
    object's upper 3x3 matrix components are replaced by the passed rotation
    components, and then the scale is reapplied to the rotational
    components.

    :param three_by_three_matrix: T precision 3x3 matrix
    """
    scale = Matrix4fSVD(NewObj)

    NewObj = Matrix4fSetRotationScaleFromMatrix3f(NewObj, three_by_three_matrix)
    scaled_NewObj = NewObj * scale  # Matrix4fMulRotationScale(NewObj, scale);
    return scaled_NewObj


def Matrix3fSetRotationFromQuat4f(q1):
    """Converts the H quaternion q1 into a new equivalent 3x3 rotation matrix."""
    X = 0
    Y = 1
    Z = 2
    W = 3

    NewObj = Matrix3fT()
    n = Numeric.sum(Numeric.dot(q1, q1))
    s = 0.0
    if (n > 0.0):
        s = 2.0 / n

    xs = q1[X] * s
    ys = q1[Y] * s
    zs = q1[Z] * s

    wx = q1[W] * xs
    wy = q1[W] * ys
    wz = q1[W] * zs

    xx = q1[X] * xs
    xy = q1[X] * ys
    xz = q1[X] * zs

    yy = q1[Y] * ys
    yz = q1[Y] * zs
    zz = q1[Z] * zs

    # This math all comes about by way of algebra, complex math, and trig identities.
    # See Lengyel pages 88-92
    NewObj[X][X] = 1.0 - (yy + zz)
    NewObj[Y][X] = xy - wz
    NewObj[Z][X] = xz + wy

    NewObj[X][Y] = xy + wz
    NewObj[Y][Y] = 1.0 - (xx + zz)
    NewObj[Z][Y] = yz - wx

    NewObj[X][Z] = xz - wy
    NewObj[Y][Z] = yz + wx
    NewObj[Z][Z] = 1.0 - (xx + yy)

    return NewObj