opengl.camera — pyFormex 1.0.5 documentation

# Source code for opengl.camera

    # $Id$
    ##
    ##  This file is part of pyFormex 1.0.5  (Sat Feb 16 10:40:32 CET 2019)
    ##  pyFormex is a tool for generating, manipulating and transforming 3D
    ##  geometrical models by sequences of mathematical operations.
    ##  Home page: http://pyformex.org
    ##  Project page:  http://savannah.nongnu.org/projects/pyformex/
    ##  Copyright 2004-2018 (C) Benedict Verhegghe (benedict.verhegghe@ugent.be)
    ##  Distributed under the GNU General Public License version 3 or later.
    ##
    ##  This program is free software: you can redistribute it and/or modify
    ##  it under the terms of the GNU General Public License as published by
    ##  the Free Software Foundation, either version 3 of the License, or
    ##  (at your option) any later version.
    ##
    ##  This program is distributed in the hope that it will be useful,
    ##  but WITHOUT ANY WARRANTY; without even the implied warranty of
    ##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    ##  GNU General Public License for more details.
    ##
    ##  You should have received a copy of the GNU General Public License
    ##  along with this program.  If not, see http://www.gnu.org/licenses/.
    ##

    """OpenGL camera handling

    Python OpenGL framework for pyFormex

    This OpenGL framework is intended to replace (in due time)
    the current OpenGL framework in pyFormex.

    (C) 2013 Benedict Verhegghe and the pyFormex project.

    """
    from __future__ import absolute_import, division, print_function

    from pyformex.opengl.matrix import Matrix4, Vector4
    from pyformex import arraytools as at
    from pyformex.coords import Coords
    from pyformex.plugins.nurbs import Coords4

    import numpy as np

    #
    # DEVS: collect all GL calls here, so we can easily move them somewhere else
    #

    import OpenGL.GL as GL

    def gl_projection():
        """Get the OpenGL projection matrix"""
        return GL.glGetDoublev(GL.GL_PROJECTION_MATRIX)
    def gl_modelview():
        """Get the OpenGL modelview matrix"""
        return GL.glGetDoublev(GL.GL_MODELVIEW_MATRIX)
    def gl_viewport():
        """Get the OpenGL viewport"""
        return GL.glGetIntegerv(GL.GL_VIEWPORT)
    def gl_loadmodelview(m):
        """Load the OpenGL modelview matrix"""
        GL.glMatrixMode(GL.GL_MODELVIEW)
        GL.glLoadMatrixf(m)
    def gl_loadprojection(m):
        """Load the OpenGL projection matrix"""
        GL.glMatrixMode(GL.GL_PROJECTION)
        GL.glLoadMatrixf(m)
        # we reset OpenGL engine to default MODELVIEW
        GL.glMatrixMode(GL.GL_MODELVIEW)
    def gl_depth(x, y):
        """Read the depth value of the pixel at (x,y)"""
        return GL.glReadPixels(x, y, 1, 1, GL.GL_DEPTH_COMPONENT, GL.GL_FLOAT)

    #
    # Normalize and denormalize should probably be moved to arraytools.
    #

    def normalize(x, w):
        """Normalized coordinates inside a window.

        Parameters:

        - `x`: an (np,nc) array with coordinates.
        - `w`: a (2,nc) array with minimal and width of the window that will
          be mapped to the range -1..1.

        Returns an array with the x values linearly remapped thus that values w[0]
        become -1 and values w[0]+w[1] become +1.
        """
        x = at.checkArray(x, (-1, -1), 'f')
        np, nc = x.shape
        w = at.checkArray(w, (2, nc), 'f', 'i')
        return (x-w[0]) * 2 / w[1] - 1

    def denormalize(x, w):
        """Map normalized coordinates to fit a window

        Parameters:

        - `x`: an (np,nc) array with normalized coordinates.
        - `w`: a (2,nc) array with minimal and width values of the window.

        Returns an array with the x values linearly remapped thus that values -1
        coincide with the minimum window values and +1 with the minimum+width
        values.
        """
        x = at.checkArray(x, (-1, -1), 'f')
        np, nc = x.shape
        w = at.checkArray(w, (2, nc), 'f', 'i')
        return w[0] + (1+x) * w[1] / 2

    def perspective_matrix(left, right, bottom, top, near, far):
        """Create a perspective Projection matrix.

        """
        m = Matrix4()
        m[0, 0] = 2 * near / (right-left)
        m[1, 1] = 2 * near / (top-bottom)
        m[2, 0] = (right+left) / (right-left)
        m[2, 1] = (top+bottom) / (top-bottom)
        m[2, 2] = - (far+near) / (far-near)
        m[2, 3] = -1.
        m[3, 2] = -2 * near * far / (far-near)
        m[3, 3] = 0.
        return m

    def orthogonal_matrix(left, right, bottom, top, near, far):
        """Create an orthogonal Projection matrix.

        """
        m = Matrix4()
        m[0, 0] = 2 / (right-left)
        m[1, 1] = 2 / (top-bottom)
        m[2, 2] = -2 / (far-near)
        m[3, 0] = - (right+left) / (right-left)
        m[3, 1] = - (top+bottom) / (top-bottom)
        m[3, 2] = - (far+near) / (far-near)
        return m

    def pick_matrix(x, y, w, h, viewport):
        """Create a pick Projection matrix

        """
        m = Matrix4()
        m[0, 0] = viewport[2] / w;
        m[1, 1] = viewport[3] / h;
        m[3, 0] = (viewport[2] + 2.0 * (viewport[0] - x)) / w;
        m[3, 1] = (viewport[3] + 2.0 * (viewport[1] - y)) / h;
        return m

    built_in_views = {
        'front': (0., 0., 0.),
        'back': (180., 0., 0.),
        'right': (90., 0., 0.),
        'left': (270., 0., 0.),
        'top': (0., 90., 0.),
        'bottom': (0., -90., 0.),
        'iso0': (45., 45., 0.),
        'iso1': (45., 135., 0.),
        'iso2': (45., 225., 0.),
        'iso3': (45., 315., 0.),
        'iso4': (-45., 45., 0.),
        'iso5': (-45., 135., 0.),
        'iso6': (-45., 225., 0.),
        'iso7': (-45., 315., 0.),
        }

    class ViewAngles(dict):
        """A dict to keep named camera angle settings.

        This class keeps a dictionary of named angle settings. Each value is
        a tuple of (longitude, latitude, twist) camera angles.
        This is a static class which should not need to be instantiated.

        There are seven predefined values: six for looking along global
        coordinate axes, one isometric view.
        """

        def __init__(self,data = built_in_views):
           dict.__init__(self, data)
           self['iso'] = self['iso0']

        def get(self, name):
            """Get the angles for a named view.

            Returns a tuple of angles (longitude, latitude, twist) if the
            named view was defined, or None otherwise
            """
            return dict.get(self, name, None)

    view_angles = ViewAngles()

    class Camera(object):
        """A camera for 3D model rendering.

        The Camera class holds all the camera parameters related to the
        rendering of a 3D scene onto a 2D canvas. These includes parameters
        related to camera position and orientation, as well as lens related
        parameters (opening angle, front and back clipping planes).
        The class provides the required matrices to transform the 3D world
        coordinates to 2D canvas coordinates, as well as a wealth of methods
        to change the camera settings in a convenient way so as to simulate
        smooth camera manipulation.

        The basic theory of camera handling and 3D rendering can be found in
        a lot of places on the internet, especially in OpenGL related places.
        However, while the pyFormex rendering engine is based on OpenGL,
        the way it stores and handles the camera parameters is more sophisticated
        than what is usually found in popular tutorials on OpenGL rendering.
        Therefore we give here a extensive description of how the pyFormex
        camera handling and 3D to 2D coordinate transformation works.

        .. note: The remainder below is obsolete and needs to be rewritten.

        Camera position and orientation:

            The camera viewing line is defined by two points: the position of
            the camera and the center of the scene the camera is looking at.
            We use the center of the scene as the origin of a local coordinate
            system to define the camera position. For convenience, this could be
            stored in spherical coordinates, as a distance value and two angles:
            longitude and latitude. Furthermore, the camera can also rotate around
            its viewing line. We can define this by a third angle, the twist.
            From these four values, the needed translation vector and rotation
            matrix for the scene rendering may be calculated.

            Inversely however, we can not compute a unique set of angles from
            a given rotation matrix (this is known as 'gimball lock').
            As a result, continuous (smooth) camera rotation by e.g. mouse control
            requires that the camera orientation be stored as the full rotation
            matrix, rather than as three angles. Therefore we store the camera
            position and orientation as follows:

            - `ctr`: `[ x,y,z ]` : the reference point of the camera:
              this is always a point on the viewing axis. Usually, it is set to
              the center of the scene you are looking at.
            - `dist`: distance of the camera to the reference point.
            - `rot`: a 3x3 rotation matrix, rotating the global coordinate system
              thus that the z-direction is oriented from center to camera.

            These values have influence on the Modelview matrix.

        Camera lens settings:

            The lens parameters define the volume that is seen by the camera.
            It is described by the following parameters:

            - `fovy`: the vertical lens opening angle (Field Of View Y),
            - `aspect`: the aspect ratio (width/height) of the lens. The product
              `fovy * aspect` is the horizontal field of view.
            - `near, far`: the position of the front and back clipping planes.
              They are given as distances from the camera and should both be
              strictly positive. Anything that is closer to the camera than
              the `near` plane or further away than the `far` plane, will not be
              shown on the canvas.

            Camera methods that change these values will not directly change
            the Modelview matrix. The :meth:`loadModelview` method has to be called
            explicitely to make the settings active.

            These values have influence on the Projection matrix.

        Methods that change the camera position, orientation or lens parameters
        will not directly change the related Modelview or Projection matrix.
        They will just flag a change in the camera settings. The changes are
        only activated by a call to the :meth:`loadModelview` or
        :meth:`loadProjection` method, which will test the flags to see whether
        the corresponding matrix needs a rebuild.

        The default camera is at distance 1.0 of the center point [0.,0.,0.] and
        looking in the -z direction.
        Near and far clipping planes are by default set to 0.1, resp 10 times
        the camera distance.

        Properties:

        - `modelview`: Matrix4: the OpenGL Modelview transformation matrix
        - `projection`: Matrix4: the OpenGL Projection transformation matrix

        """

        # DEVELOPERS:
        #    The camera class assumes that matrixmode is always Modelview on entry.
        #    For operations in other modes, an explicit switch before the operations
        #    and afterwards back to Modelview should be performed.

        def __init__(self,focus=[0., 0., 0.],angles=[0., 0., 0.],dist=1.):
            """Create a new camera.

            The default camera is positioned at (0.,0.,1.) looking along the -z
            axis in the direction of the point (0.,0.,0.) and with the upvector
            in the direction of the y-axis.
            """
            self.locked = False

            self._modelview = Matrix4()
            self.focus = focus
            self.dist = dist
            self.viewChanged = True

            self._projection = Matrix4()
            self._perspective = True
            self.lensChanged = True

            self.setModelview(angles=angles)
            self.setLens(45., 4./3.)
            self.setClip(0.1, 10.)
            self.area = None
            self.resetArea()
            self.keep_aspect = True
            self.tracking = False
            self.p = self.v = None

        @property
        def modelview(self):
            """Return the current modelview matrix.

            This will recompute the modelview matrix if any camera position
            parameters have changed.
            """
            if self.viewChanged:
                self.setModelview()
            return self._modelview

        @modelview.setter
        def modelview(self, value):
            """Set the modelview matrix to the specified matrix.

            value should be a proper modelview matrix
            """
            self._modelview = Matrix4(value)

        @property
        def projection(self):
            """Return the current projection matrix.

            This will recompute the projection matrix if any camera lens
            parameters have changed.
            """
            if self.lensChanged:
                self.setProjection()
            return self._projection

        @projection.setter
        def projection(self, value):
            """Set the projection matrix to the specified matrix.

            value should be a proper projection matrix
            """
            self._projection = Matrix4(value)

        @property
        def viewport(self):
            """Return the camera viewport.

            This property can not be changed directly.
            It should be changed by resizing the parent canvas.
            """
            return gl_viewport()

        @property
        def focus(self):
            """Return the camera reference point (the focus point)."""
            return self._focus

        @focus.setter
        def focus(self, vector):
            """Set the camera reference point (the focus point).

            The focus is the point the camer is looking at. It is a point on
            the camera's optical axis.

            - `vector`: (3,) float array: the global coordinates of the focus.

            """
            if not self.locked:
                self._focus = at.checkArray(vector, (3,), 'f')
                self.viewChanged = True

        @property
        def dist(self):
            """Return the camera distance.

            The camera distance is the distance between the camera eye and
            the camera focus point.
            """
            return self._dist

        @dist.setter
        def dist(self, dist):
            """Set the camera distance.

            - `dist`: a strictly positive float value. Invalid values are
            silently ignored.
            """
            if not self.locked:
                if dist > 0.0 and dist != np.inf:
                    self._dist = dist
                    self.viewChanged = True

        @property
        def perspective(self,on=True):
            """Return the perspecive flag.

            If the perspective flag is True, the camera uses a perspective
            projection. If it is False, the camera uses orthogonal projection.
            """
            return self._perspective

        @perspective.setter
        def perspective(self, flag):
            """Set the perspecive flag.

            - `flag`: bool, the value to set the perspective flag to.

            If changed, this forces the recalculation of the projection matrix.
            """
            if not self.locked:
                if flag != self._perspective:
                    self._perspective = bool(flag)
                    self.lensChanged = True

        @property
        def rot(self):
            """Return the camera rotation matrix."""
            return self.modelview.rot

        @property
        def upvector(self):
            """Return the camera up vector"""
            return self.modelview.rot[:, 1].reshape((3,))

        @property
        def axis(self):
            """Return a unit vector along the camera axis.

            The camera axis points from the focus towards the camera.
            """
            # this is the same as: at.normalize(self.eye-self.focus)
            return self.modelview.rot[:, 2].reshape((3,))

        def setAngles(self, angles):
            """Set the rotation angles.

            angles is either:

            - a tuple of angles (long,lat,twist)
            - a named view corresponding to angles in view_angles
            - None
            """
            if not self.locked:
                if isinstance(angles, str):
                    angles = view_angles.get(angles)
                if angles is None:
                    return
                self.setModelview(angles=angles)

        @property
        def eye(self):
            """Return the position of the camera."""
            return self.toWorld([0., 0., 0.])

        @eye.setter
        def eye(self,eye):
            """Set the position of the camera."""
            return self.lookAt(eye=eye)

        def lock(self,onoff=True):
            """Lock/unlock a camera.

            When a camera is locked, its position and lens parameters can not be
            changed.
            This can e.g. be used in multiple viewports layouts to create fixed
            views from different angles.
            """
            self.locked = bool(onoff)

        def unlock(self):
            self.lock(False)

        def report(self):
            """Return a report of the current camera settings."""
            return """Camera Settings:
      Eye: %s
      Focus: %s
      Distance: %s
      Axis: %s
      UpVector: %s
      Rotation Matrix:
      %s
      Field of View y: %s
      Aspect Ratio: %s
      Area: %s, %s
      Near/Far Clip: %s, %s
    """ % (self.eye, self.focus, self.dist, self.axis, self.upvector, self.rot, self.fovy, self.aspect, self.area[0], self.area[1], self.near, self.far)

        def dolly(self, val):
            """Move the camera eye towards/away from the scene center.

            This has the effect of zooming. A value > 1 zooms out,
            a value < 1 zooms in. The resulting enlargement of the view
            will approximately be 1/val.
            A zero value will move the camera to the center of the scene.
            The front and back clipping planes may need adjustment after
            a dolly operation.
            """
            if not self.locked:
                self.dist *= val
                self.viewChanged = True

        # TODO: This is broken!
        def pan(self,val,axis=0):
            """Rotate the camera around axis through its eye.

            The camera is rotated around an axis through the eye point.
            For axes 0 and 1, this will move the focus, creating a panning
            effect. The default axis is parallel to the y-axis, resulting in
            horizontal panning. For vertical panning (axis=1) a convenience
            alias tilt is created.
            For axis = 2 the operation is equivalent to the rotate operation.
            """
            if not self.locked:
                if axis==0 or axis ==1:
                    pos = self.eye
                    self.eye[axis] = (self.eye[axis] + val) % 360
                    print(self.report())
                    self.focus = diff(pos, sphericalToCartesian(self.eye))
                    print(self.report())
                elif axis==2:
                    print(self.report())
                    self.twist = (self.twist + val) % 360
                self.viewChanged = True

        # TODO: THis depends on the broken pan!
        def tilt(self, val):
            """Rotate the camera up/down around its own horizontal axis.

            The camera is rotated around and perpendicular to the plane of the
            y-axis and the viewing axis. This has the effect of a vertical pan.
            A positive value tilts the camera up, shifting the scene down.
            The value is specified in degrees.
            """
            if not self.locked:
                self.pan(val, 1)
                self.viewChanged = True

        def move(self, dx, dy, dz):
            """Move the camera over translation (dx,dy,dz) in global coordinates.

            The focus of the camera is moved over the specified translation
            vector. This has the effect of moving the scene in opposite direction.
            """
            if not self.locked:
                x, y, z = self.ctr
                self.focus += [dx, dy, dz]

    ##    def truck(self,dx,dy,dz):
    ##        """Move the camera translation vector in local coordinates.

    ##        This has the effect of moving the scene in opposite direction.
    ##        Positive coordinates mean:
    ##          first  coordinate : truck right,
    ##          second coordinate : pedestal up,
    ##          third  coordinate : dolly out.
    ##        """
    ##        #pos = self.position
    ##        ang = self.getAngles()
    ##        tr = [dx,dy,dz]
    ##        for i in [1,0,2]:
    ##            r = rotationMatrix(i,ang[i])
    ##            tr = multiply(tr, r)
    ##        self.move(*tr)
    ##        self.viewChanged = True

        # TODO
        def translate(self,vx,vy,vz,local=True):
            if not self.locked:
                if local:
                    vx, vy, vz = self.toWorld([vx, vy, vz, 1])
                self.move(-vx, -vy, -vz)

        def setLens(self,fovy=None,aspect=None):
            """Set the field of view of the camera.

            We set the field of view by the vertical opening angle fovy
            and the aspect ratio (width/height) of the viewing volume.
            A parameter that is not specified is left unchanged.
            """
            if fovy:
                self.fovy = min(abs(fovy), 180)
            if aspect:
                self.aspect = abs(aspect)
            self.lensChanged = True

        def resetArea(self):
            """Set maximal camera area.

            Resets the camera window area to its maximum values corresponding
            to the fovy setting, symmetrical about the camera axes.
            """
            self.setArea(0., 0., 1., 1., False)

        def setArea(self,hmin,vmin,hmax,vmax,relative=True,focus=False,center=False,clip=True):
            """Set the viewable area of the camera.

            Note: Use relative=False and clip=False if you want to set the zoom
            exactly as in previously recorded values.
            """
            area = np.array([hmin, vmin, hmax, vmax])
            if clip:
                area = area.clip(0., 1.)
            if area[0] < area[2] and area[1] < area[3]:
                area = area.reshape(2, 2)
                mean = (area[1]+area[0]) * 0.5
                diff = (area[1]-area[0]) * 0.5

                if relative:
                    if self.keep_aspect:
                        aspect = diff[0] / diff[1]
                        if aspect > 1.0:
                            diff[1] = diff[0] #/ self.aspect
                            # no aspect factor: this is relative!!!
                        else:
                            diff[0] = diff[1] #* self.aspect
                    if focus:
                        mean = np.zeros(2)
                    area[0] = mean-diff
                    area[1] = mean+diff
                    #print("RELATIVE AREA %s" % (area))
                    area = (1.-area) * self.area[0] + area * self.area[1]

                if center:
                    # make center of area equal to 0.5,0.5
                    mean = (area[1]+area[0]) * 0.5
                    area += 0.5-mean

                #print("OLD ZOOM AREA %s (aspect %s)" % (self.area,self.aspect))
                #print("NEW ZOOM AREA %s" % (area))

                self.area = area
                self.lensChanged = True

        def zoomArea(self,val=0.5,area=None):
            """Zoom in/out by shrinking/enlarging the camera view area.

            The zoom factor is relative to the current setting.
            Values smaller than 1.0 zoom in, larger values zoom out.
            """
            if val>0:
                #val = (1.-val) * 0.5
                #self.setArea(val,val,1.-val,1.-val,focus=focus)
                if area is None:
                    area = self.area
                #print("ZOOM AREA %s (%s)" % (area.tolist(),val))
                mean = (area[1]+area[0]) * 0.5
                diff = (area[1]-area[0]) * 0.5 * val
                area[0] = mean-diff
                area[1] = mean+diff
                self.area = area
                #print("CAMERA AREA %s" % self.area.tolist())
                self.lensChanged = True

        def transArea(self, dx, dy):
            """Pan by moving the vamera area.

            dx and dy are relative movements in fractions of the
            current area size.
            """
            #print("TRANSAREA %s,%s" % (dx,dy))
            area = self.area
            diff = (area[1]-area[0]) * np.array([dx, dy])
            area += diff
            self.area = area
            self.lensChanged = True

        def setClip(self, near, far):
            """Set the near and far clipping planes"""
            if near > 0 and near < far:
                self.near, self.far = near, far
                self.lensChanged = True
            else:
                print("Error: Invalid Near/Far clipping values")

        ## def setClipRel(self,near,far):
        ##     """Set the near and far clipping planes"""
        ##     if near > 0 and near < far:
        ##         self.near,self.far = near,far
        ##         self.lensChanged = True
        ##     else:
        ##         print("Error: Invalid Near/Far clipping values")

        ## def zoom(self,val=0.5):
        ##     """Zoom in/out by shrinking/enlarging the camera view angle.

        ##     The zoom factor is relative to the current setting.
        ##     Use setFovy() to specify an absolute setting.
        ##     """
        ##     if val>0:
        ##         self.fovy *= val
        ##     self.lensChanged = True

        #### global manipulation ###################

        def setTracking(self,onoff=True):
            """Enable/disable coordinate tracking using the camera"""
            if onoff:
                self.tracking = True
                #self.set3DMatrices()
            else:
                self.tracking = False

    #################################################################
    ##  Operations on modelview matrix  ##

        def setProjection(self):
            """Set the projection matrix.

            This computes and sets the camera's projection matrix, depending
            on the current camera settings. The projection can either be
            an orthogonal or a perspective one.

            The computed matrix is saved as the camera's projection matrix,
            and the lensChanged attribute is set to False.

            The matrix can be retrieved from the projection attribute,
            and can be loaded in the GL context with loadProjection().

            This function does nothing if the camera is locked.
            """
            if self.locked:
                return

            fv = at.tand(self.fovy*0.5)
            if self._perspective:
                fv *= self.near
            else:
                fv *= self.dist
            fh = fv * self.aspect
            x0, x1 = 2*self.area - 1.0
            frustum = (fh*x0[0], fh*x1[0], fv*x0[1], fv*x1[1], self.near, self.far)
            if self._perspective:
                func = perspective_matrix
            else:
                func = orthogonal_matrix
            self.projection = func(*frustum)

            try:
                self.projection_callback(self)
            except:
                pass
            self.lensChanged = False

        def loadProjection(self):
            """Load the Projection matrix.

            If lens parameters of the camera have been changed, the current
            Projection matrix is rebuild.
            Then, the current Projection matrix of the camera is loaded into the
            OpenGL engine.
            """
            gl_loadprojection(self.projection.gl())

        def pickMatrix(self,rect,viewport=None):
            """Return a picking matrix.

            The picking matrix confines the scope of the normalized device
            coordinates to a rectangular subregion of the camera viewport.
            This means that values in the range -1 to +1 are inside the
            rectangle.

            Parameters:

            - `rect`: a tuple of 4 floats (x,y,w,h) defining the picking region
              center (x,y) and size (w,h)
            - `viewport`: a tuple of 4 int values (xmin,ymin,xmax,ymax) defining
              the size of the viewport. This is normally left unspecified and
              set to the camera viewport.
            """
            if viewport is None:
                viewport = self.viewport
            return pick_matrix(rect[0], rect[1], rect[2], rect[3], viewport)

        def eyeToClip(self, x):
            """Transform a vertex from eye to clip coordinates.

            This transforms the vertex using the current Projection matrix.

            It is equivalent with multiplying the homogeneous
            coordinates with the Projection matrix, but is done here
            in an optimized way.
            """
            return self.projection.transform(x)

        def clipToEye(self, x):
            """Transform a vertex from clip to eye coordinates.

            This transforms the vertex using the inverse of the
            current Projection matrix.

            It is equivalent with multiplying the homogeneous
            coordinates with the inverse Projection matrix, but is done
            here in an optimized way.
            """
            return self.projection.invtransform(x)

    #################################################################
    ##  Operations on modelview matrix  ##

        def lookAt(self,focus=None,eye=None,up=None):
            """Set the Modelview matrix to look at the specified focus point.

            The Modelview matrix is set with the camera positioned at eye
            and looking at the focus points, while the camera up vector is
            in the plane of the camera axis (focus-eye) and the specified
            up vector.

            If any of the arguments is left unspecified, the current value
            will be used.
            """
            if not self.locked:
                if focus is None:
                    focus = self.focus
                else:
                    focus = at.checkArray(focus, (3,), 'f')
                if eye is None:
                    eye = self.eye
                else:
                    eye = at.checkArray(eye, (3,), 'f')
                if up is None:
                    up = self.upvector
                else:
                    up = at.normalize(at.checkArray(up, (3,), 'f'))
                vector = eye-focus
                self.focus = focus
                self.dist = at.length(vector)
                axis2 = at.normalize(vector)
                axis0 = at.normalize(np.cross(up, axis2))
                axis1 = at.normalize(np.cross(axis2, axis0))
                m = Matrix4()
                m.rotate(np.column_stack([axis0, axis1, axis2]))
                m.translate(-eye)
                self.setModelview(m)

        def rotate(self, val, vx, vy, vz):
            """Rotate the camera around current camera axes."""
            if not self.locked:
                rot = self._modelview.rot
                m = Matrix4()
                m.translate([0, 0, -self.dist])
                m.rotate(val % 360, [vx, vy, vz])
                m.rotate(rot)
                m.translate(-self.focus)
                self.setModelview(m)

        def setModelview (self,m=None,angles=None):
            """Set the Modelview matrix.

            The Modelview matrix can be set from one of the following sources:

            - if `mat` is specified, it is a 4x4 matrix with a valuable
              Modelview transformation. It will be set as the current camera
              Modelview matrix.

            - else, if `angles` is specified, it is a sequence of the three
              camera angles (latitude, longitude and twist). The camera
              Modelview matrix is set from the current camera focus,
              the current camera distance, and the specified angles.
              This option is typically used to change the viewing direction
              of the camera, while keeping the focus point and camera distance.

            - else, if the viewChanged flags is set, the camera Modelview
              matrix is set from the current camera focus, the current camera
              distance, and the current camera rotation matrix.
              This option is typically used after changing the camera focus
              point and/or distance, while keeping the current viewing angles.

            - else, the current Modelview matrix remains unchanged.

            In all cases, if a modelview callback was set, it is called,
            and the viewChanged flag is cleared.
            """
            if self.locked:
                return

            if m is None and (self.viewChanged or angles is not None):
                m = Matrix4()
                m.translate([0, 0, -self.dist])
                if angles is None:
                    m.rotate(self._modelview.rot)
                else:
                    long, lat, twist = angles
                    m.rotate(-twist % 360, [0.0, 0.0, 1.0])
                    m.rotate(lat % 360, [1.0, 0.0, 0.0])
                    m.rotate(-long % 360, [0.0, 1.0, 0.0])
                m.translate(-self.focus)

            if m is not None:
                self.modelview = m

            try:
                self.modelview_callback(self)
            except:
                pass
            self.viewChanged = False

        def loadModelview (self):
            """Load the Modelview matrix.

            If camera positioning parameters have been changed, the current
            Modelview matrix is rebuild.
            Then, the current Modelview matrix of the camera is loaded into the
            OpenGL engine.
            """
            gl_loadmodelview(self.modelview.gl())

        def toEye(self, x):
            """Transform a vertex from world to eye coordinates.

            This transforms the vertex using the current Modelview matrix.

            It is equivalent with multiplying the homogeneous
            coordinates with the Modelview matrix, but is done here
            in an optimized way.
            """
            x = at.checkArray(x, (-1,3), 'f')
            return np.dot(x, self.modelview[:3, :3]) + self.modelview[3, :3]

        def toWorld(self, x):
            """Transform a vertex from eye to world coordinates.

            This transforms the vertex using the inverse of the
            current Modelview matrix.

            It is equivalent with multiplying the homogeneous
            coordinates with the inverse Modelview matrix, but is done
            here in an optimized way.
            """
            x = at.checkArray(x, (3,), 'f') + [0., 0., self.dist]
            return np.dot(x, self.rot.T) + self.focus

    #################################################################
    ##  Transform vertices with modelview and projection matrix  ##

        def toWindow(self, x):
            """Convert normalized device coordinates to window coordinates"""
            # This is only correct when glDepthRange(0.0, 1.0)
            # We should not change the depth range
            vp = gl_viewport()
            #print([[vp[0], vp[1], 0], [vp[2], vp[3], 1]])
            return denormalize(x[:, :3], [[vp[0], vp[1], 0], [vp[2], vp[3], 1]])

        def fromWindow(self, x):
            """Convert window coordinates to  normalized device coordinates"""
            # This is only correct when glDepthRange(0.0, 1.0)
            # We should not change the depth range
            vp = gl_viewport()
            x = at.checkArray(x,(-1,3),'f')
            return normalize(x[:, :3], [[vp[0], vp[1], 0], [vp[2], vp[3], 1]])

        def toNDC(self,x,rect=None):
            """Convert world coordinates to normalized device coordinates.

            The normalized device coordinates (NDC) have x and y values
            in the range -1 to +1 for points that are falling within the
            visible region of the camera.

            Parameters:

            - `x`: Coords with the world coordinates to be converted
            - `rect`: optional, a tuple of 4 values (x,y,w,h) specifying
              a rectangular subregion of the camera's viewport. The default
              is the full camera viewport.

            The return value is a Coords. The z-coordinate provides
            depth information.
            """
            m = self.modelview*self.projection
            if rect is not None:
                m = m*self.pickMatrix(rect)
            x = Coords4(x)
            x = Coords4(np.dot(x, m))
            if self._perspective:
                x = x.toCoords() # This performs the perspective divide
            else:
                # Orthogonal projection
                # This is not tested yet!!!
                x = Coords(x[..., :3])
            return x

        def toNDC1(self,x,rect=None):
            """This is like toNDC without the perspective divide

            This function is useful to compute the vertex position of a
            3D point as computed by the vertex shader.

            """
            m = self.modelview*self.projection
            if rect is not None:
                m = m*self.pickMatrix(rect)
            x = Coords4(x)
            x = Coords4(np.dot(x, m))
            x = Coords(x[..., :3])
            return x

        def project(self, x):
            """Map the world coordinates (x,y,z) to window coordinates."""
            #m = self.modelview*self.projection
            # Modelview transform
            e = Vector4(x)*self.modelview
            #print("EYE COORDINATES:",e)
            w = -e[:, 2]
            # Projection
            x = e*self.projection
            #print("CLIP COORDINATES:",x)
            # Perspective division
            if self._perspective:
                ## if (w == 0.0):
                ##     return [np.inf,np.inf,np.inf]
                x = x/w
            #print("NORMALIZED DEVICE COORDINATES:",x)
            # Map to window
            return self.toWindow(x)

        def unproject(self, x):
            """Map the window coordinates x to object coordinates."""
            m = self.modelview*self.projection
            #print("M*P",m)
            m1 = np.linalg.inv(m)
            #print("M*P -1",m1)
            x = self.fromWindow(x)
            #print("NORMALIZED DEVICE COORDINATES:",x)
            x = Vector4(x)*m1
            return Coords(x[:, :3] / x[:, 3])

        def inside(self,x,rect=None,return_depth=False):
            """Test if points are visible inside camera.

            Parameters:

            - `rect`: optional, a tuple of 4 values (x,y,w,h) specifying
              a rectangular subregion of the camera's viewport. The default
              is the full camera viewport.
            - `return_depth`: if True, also returns the the z-depth of the
              points.

            Returns a boolean array with value 1 (True) for the points that
            are projected inside the rectangular are of the camera.
            If `return_depth` is True, a second array with the z-depth value
            of all the points is returned.
            """
            ndc = self.toNDC(x, rect)
            # TODO: WHY THE abs ?????
            xy = ndc[:, :2]
            inside = ( xy >= -1 ).all(axis=-1) * ( xy <= 1 ).all(axis=-1)
            if return_depth:
                return inside, ndc[:, 2]
            else:
                return inside

    #################################
        # Compatibility: should be removed after complete conversion

        def getGLmodelview(self):
            return Matrix4(GL.glGetDoublev(GL.GL_MODELVIEW_MATRIX))

        def getGLprojection(self):
            return Matrix4(GL.glGetDoublev(GL.GL_PROJECTION_MATRIX))

        loadModelView = loadModelview
        def saveModelView(self):
            pass
        def set3DMatrices(self):
            self.loadProjection()
            self.loadModelView()
            #print("MODELVIEW",self.modelview)
            #print("MODELVIEW",self.getGLmodelview())
            #print("PROJECTION",self.projection)
            #print("PROJECTION",self.getGLprojection())

        def setPerspective(self,on=True):
            self.perspective = on

    # End