#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Tools for working with view projections for 2- and 3-D rendering.
"""
# Part of the PsychoPy library
# Copyright (C) 2002-2018 Jonathan Peirce (C) 2019-2024 Open Science Tools Ltd.
# Distributed under the terms of the GNU General Public License (GPL).
__all__ = ['Frustum',
'visualAngle',
'computeFrustum',
'computeFrustumFOV',
'projectFrustum',
'projectFrustumToPlane',
'generalizedPerspectiveProjection',
'orthoProjectionMatrix',
'perspectiveProjectionMatrix',
'lookAt',
'pointToNdc',
'cursorToRay',
'visible',
'visibleBBox']
import numpy as np
from collections import namedtuple
import psychopy.tools.mathtools as mt
DEG_TO_RAD = np.pi / 360.0
VEC_FWD_AND_UP = np.array(((0., 0., -1.), (0., 1., 0.)), dtype=np.float32)
[docs]def visualAngle(size, distance, degrees=True, out=None, dtype=None):
"""Get the visual angle for an object of `size` at `distance`. Object is
assumed to be fronto-parallel with the viewer.
This function supports vector inputs. Values for `size` and `distance` can
be arrays or single values. If both inputs are arrays, they must have the
same size.
Parameters
----------
size : float or array_like
Size of the object in meters.
distance : float or array_like
Distance to the object in meters.
degrees : bool
Return result in degrees, if `False` result will be in radians.
out : ndarray, optional
Optional output array. Must be same `shape` and `dtype` as the expected
output if `out` was not specified.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
float
Visual angle.
Examples
--------
Calculating the visual angle (vertical FOV) of a monitor screen::
monDist = 0.5 # monitor distance, 50cm
monHeight = 0.45 # monitor height, 45cm
vertFOV = visualAngle(monHeight, monDist)
Compute visual angle at multiple distances for objects with the same size::
va = visualAngle(0.20, [1.0, 2.0, 3.0]) # returns
# [11.42118627 5.72481045 3.81830487]
"""
if out is None:
dtype = np.float64 if dtype is None else np.dtype(dtype).type
else:
dtype = np.dtype(out.dtype).type
size, distance = np.atleast_1d(size, distance)
if out is not None:
out[:] = 2 * np.arctan(size / (2 * distance), dtype=dtype)
if degrees:
out[:] = np.degrees(out, dtype=dtype)
toReturn = out
else:
toReturn = 2 * np.arctan(size / (2 * distance), dtype=dtype)
if degrees:
toReturn[:] = np.degrees(toReturn, dtype=dtype)
return toReturn
# convenient named tuple for storing frustum parameters
Frustum = namedtuple(
'Frustum',
['left', 'right', 'bottom', 'top', 'nearVal', 'farVal'])
[docs]def computeFrustum(scrWidth,
scrAspect,
scrDist,
convergeOffset=0.0,
eyeOffset=0.0,
nearClip=0.01,
farClip=100.0,
dtype=None):
"""Calculate frustum parameters. If an eye offset is provided, an asymmetric
frustum is returned which can be used for stereoscopic rendering.
Parameters
----------
scrWidth : float
The display's width in meters.
scrAspect : float
Aspect ratio of the display (width / height).
scrDist : float
Distance to the screen from the view in meters. Measured from the center
of their eyes.
convergeOffset : float
Offset of the convergence plane from the screen. Objects falling on this
plane will have zero disparity. For best results, the convergence plane
should be set to the same distance as the screen (0.0 by default).
eyeOffset : float
Half the inter-ocular separation (i.e. the horizontal distance between
the nose and center of the pupil) in meters. If eyeOffset is 0.0, a
symmetric frustum is returned.
nearClip : float
Distance to the near clipping plane in meters from the viewer. Should be
at least less than `scrDist`.
farClip : float
Distance to the far clipping plane from the viewer in meters. Must be
>nearClip.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray
Array of frustum parameters. Can be directly passed to
glFrustum (e.g. glFrustum(*f)).
Notes
-----
* The view point must be transformed for objects to appear correctly.
Offsets in the X-direction must be applied +/- eyeOffset to account for
inter-ocular separation. A transformation in the Z-direction must be
applied to account for screen distance. These offsets MUST be applied to
the GL_MODELVIEW matrix, not the GL_PROJECTION matrix! Doing so may break
lighting calculations.
Examples
--------
Creating a frustum and setting a window's projection matrix::
scrWidth = 0.5 # screen width in meters
scrAspect = win.size[0] / win.size[1]
scrDist = win.scrDistCM * 100.0 # monitor setting, can be anything
frustum = viewtools.computeFrustum(scrWidth, scrAspect, scrDist)
Accessing frustum parameters::
left, right, bottom, top, nearVal, farVal = frustum
# ... or ...
left = frustum.left
Off-axis frustums for stereo rendering::
# compute view matrix for each eye, these value usually don't change
eyeOffset = (-0.035, 0.035) # +/- IOD / 2.0
scrDist = 0.50 # 50cm
scrWidth = 0.53 # 53cm
scrAspect = 1.778
leftFrustum = viewtools.computeFrustum(
scrWidth, scrAspect, scrDist, eyeOffset[0])
rightFrustum = viewtools.computeFrustum(
scrWidth, scrAspect, scrDist, eyeOffset[1])
# make sure your view matrix accounts for the screen distance and eye
# offsets!
Using computed view frustums with a window::
win.projectionMatrix = viewtools.perspectiveProjectionMatrix(*frustum)
# generate a view matrix looking ahead with correct viewing distance,
# origin is at the center of the screen. Assumes eye is centered with
# the screen.
eyePos = [0.0, 0.0, scrDist]
screenPos = [0.0, 0.0, 0.0] # look at screen center
eyeUp = [0.0, 1.0, 0.0]
win.viewMatrix = viewtools.lookAt(eyePos, screenPos, eyeUp)
win.applyViewTransform() # call before drawing
"""
# mdc - uses display size instead of the horizontal FOV gluPerspective needs
d = scrWidth / 2.0
ratio = nearClip / float((convergeOffset + scrDist))
right = (d - eyeOffset) * ratio
left = (d + eyeOffset) * -ratio
top = d / float(scrAspect) * ratio
bottom = -top
return np.asarray((left, right, bottom, top, nearClip, farClip),
dtype=dtype)
[docs]def computeFrustumFOV(scrFOV,
scrAspect,
scrDist,
convergeOffset=0.0,
eyeOffset=0.0,
nearClip=0.01,
farClip=100.0,
dtype=None):
"""Compute a frustum for a given field-of-view (FOV).
Similar to `computeFrustum`, but computes a frustum based on FOV rather than
screen dimensions.
Parameters
----------
scrFOV : float
Vertical FOV in degrees (fovY).
scrAspect : float
Aspect between the horizontal and vertical FOV (ie. fovX / fovY).
scrDist : float
Distance to the screen from the view in meters. Measured from the center
of the viewer's eye(s).
convergeOffset : float
Offset of the convergence plane from the screen. Objects falling on this
plane will have zero disparity. For best results, the convergence plane
should be set to the same distance as the screen (0.0 by default).
eyeOffset : float
Half the inter-ocular separation (i.e. the horizontal distance between
the nose and center of the pupil) in meters. If eyeOffset is 0.0, a
symmetric frustum is returned.
nearClip : float
Distance to the near clipping plane in meters from the viewer. Should be
at least less than `scrDist`. Never should be 0.
farClip : float
Distance to the far clipping plane from the viewer in meters. Must be
>nearClip.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Examples
--------
Equivalent to `gluPerspective`::
frustum = computeFrustumFOV(45.0, 1.0, 0.5)
projectionMatrix = perspectiveProjectionMatrix(*frustum)
"""
d = np.tan(scrFOV * DEG_TO_RAD)
ratio = nearClip / float((convergeOffset + scrDist))
right = (d - eyeOffset) * ratio
left = (d + eyeOffset) * -ratio
top = d / float(scrAspect) * ratio
bottom = -top
return np.asarray((left, right, bottom, top, nearClip, farClip),
dtype=dtype)
[docs]def projectFrustum(frustum, dist, dtype=None):
"""Project a frustum on a fronto-parallel plane and get the width and height
of the required drawing area.
This function can be used to determine the size of the drawing area required
for a given frustum on a screen. This is useful for cases where the observer
is viewing the screen through a physical aperture that limits the FOV to a
sub-region of the display. You must convert the size in meters to units of
your screen and apply any offsets.
Parameters
----------
frustum : array_like
Frustum parameters (left, right, bottom, top, near, far), you can
exclude `far` since it is not used in this calculation. However, the
function will still succeed if given.
dist : float
Distance to project points to in meters.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray
Width and height (w, h) of the area intersected by the given frustum at
`dist`.
Examples
--------
Compute the viewport required to draw in the area where the frustum
intersects the screen::
# needed information
scrWidthM = 0.52
scrDistM = 0.72
scrWidthPIX = 1920
scrHeightPIX = 1080
scrAspect = scrWidthPIX / float(scrHeightPIX)
pixPerMeter = scrWidthPIX / scrWidthM
# Compute a frustum for 20 degree vertical FOV at distance of the
# screen.
frustum = computeFrustumFOV(20., scrAspect, scrDistM)
# get the dimensions of the frustum
w, h = projectFrustum(frustum, scrDistM) * pixPerMeter
# get the origin of the viewport, relative to center of screen.
x = (scrWidthPIX - w) / 2.
y = (scrHeightPIX - h) / 2.
# if there is an eye offset ...
# x = (scrWidthPIX - w + eyeOffsetM * pixPerMeter) / 2.
# viewport rectangle
rect = np.asarray((x, y, w, h), dtype=int)
You can then set the viewport/scissor rectangle of the buffer to restrict
drawing to `rect`.
"""
dtype = np.float64 if dtype is None else np.dtype(dtype).type
frustum = np.asarray(frustum, dtype=dtype)
l, r, t, b = np.abs(frustum[:4] * dist / frustum[4], dtype=dtype)
return np.array((l + r, t + b), dtype=dtype)
[docs]def projectFrustumToPlane(frustum, planeOrig, dtype=None):
"""Project a frustum on a fronto-parallel plane and get the coordinates of
the corners in physical space.
Parameters
----------
frustum : array_like
Frustum parameters (left, right, bottom, top, near, far), you can
exclude `far` since it is not used in this calculation. However, the
function will still succeed if given.
planeOrig : float
Distance of plane to project points on in meters.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray
4x3 array of coordinates in the physical reference frame with origin
at the eye.
"""
dtype = np.float64 if dtype is None else np.dtype(dtype).type
frustum = np.asarray(frustum, dtype=dtype)
l, r, t, b = frustum[:4] * planeOrig / frustum[4]
d = -planeOrig
return np.array(((l, t, d), (l, b, d), (r, b, d), (r, t, d)), dtype=dtype)
[docs]def generalizedPerspectiveProjection(posBottomLeft,
posBottomRight,
posTopLeft,
eyePos,
nearClip=0.01,
farClip=100.0,
dtype=None):
"""Generalized derivation of projection and view matrices based on the
physical configuration of the display system.
This implementation is based on Robert Kooima's 'Generalized Perspective
Projection' method [1]_.
Parameters
----------
posBottomLeft : list of float or ndarray
Bottom-left 3D coordinate of the screen in meters.
posBottomRight : list of float or ndarray
Bottom-right 3D coordinate of the screen in meters.
posTopLeft : list of float or ndarray
Top-left 3D coordinate of the screen in meters.
eyePos : list of float or ndarray
Coordinate of the eye in meters.
nearClip : float
Near clipping plane distance from viewer in meters.
farClip : float
Far clipping plane distance from viewer in meters.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
tuple
The 4x4 projection and view matrix.
See Also
--------
computeFrustum : Compute frustum parameters.
Notes
-----
* The resulting projection frustums are off-axis relative to the center of
the display.
* The returned matrices are row-major. Values are floats with 32-bits
of precision stored as a contiguous (C-order) array.
References
----------
.. [1] Kooima, R. (2009). Generalized perspective projection. J. Sch.
Electron. Eng. Comput. Sci.
Examples
--------
Computing a projection and view matrices for a window::
projMatrix, viewMatrix = viewtools.generalizedPerspectiveProjection(
posBottomLeft, posBottomRight, posTopLeft, eyePos)
# set the window matrices
win.projectionMatrix = projMatrix
win.viewMatrix = viewMatrix
# before rendering
win.applyEyeTransform()
Stereo-pair rendering example from Kooima (2009)::
# configuration of screen and eyes
posBottomLeft = [-1.5, -0.75, -18.0]
posBottomRight = [1.5, -0.75, -18.0]
posTopLeft = [-1.5, 0.75, -18.0]
posLeftEye = [-1.25, 0.0, 0.0]
posRightEye = [1.25, 0.0, 0.0]
# create projection and view matrices
leftProjMatrix, leftViewMatrix = generalizedPerspectiveProjection(
posBottomLeft, posBottomRight, posTopLeft, posLeftEye)
rightProjMatrix, rightViewMatrix = generalizedPerspectiveProjection(
posBottomLeft, posBottomRight, posTopLeft, posRightEye)
"""
# get data type of arrays
dtype = np.float64 if dtype is None else np.dtype(dtype).type
# convert everything to numpy arrays
posBottomLeft = np.asarray(posBottomLeft, dtype=dtype)
posBottomRight = np.asarray(posBottomRight, dtype=dtype)
posTopLeft = np.asarray(posTopLeft, dtype=dtype)
eyePos = np.asarray(eyePos, dtype=dtype)
# orthonormal basis of the screen plane
vr = posBottomRight - posBottomLeft
vr /= np.linalg.norm(vr)
vu = posTopLeft - posBottomLeft
vu /= np.linalg.norm(vu)
vn = np.cross(vr, vu)
vn /= np.linalg.norm(vn)
# screen corner vectors
va = posBottomLeft - eyePos
vb = posBottomRight - eyePos
vc = posTopLeft - eyePos
dist = -np.dot(va, vn)
nearOverDist = nearClip / dist
left = np.dot(vr, va) * nearOverDist
right = np.dot(vr, vb) * nearOverDist
bottom = np.dot(vu, va) * nearOverDist
top = np.dot(vu, vc) * nearOverDist
# projection matrix to return
projMat = perspectiveProjectionMatrix(
left, right, bottom, top, nearClip, farClip, dtype=dtype)
# view matrix to return, first compute the rotation component
rotMat = np.zeros((4, 4), dtype=dtype)
rotMat[0, :3] = vr
rotMat[1, :3] = vu
rotMat[2, :3] = vn
rotMat[3, 3] = 1.0
transMat = np.identity(4, dtype=dtype)
transMat[:3, 3] = -eyePos
return projMat, np.matmul(rotMat, transMat)
[docs]def orthoProjectionMatrix(left, right, bottom, top, nearClip=0.01, farClip=100.,
out=None, dtype=None):
"""Compute an orthographic projection matrix with provided frustum
parameters.
Parameters
----------
left : float
Left clipping plane coordinate.
right : float
Right clipping plane coordinate.
bottom : float
Bottom clipping plane coordinate.
top : float
Top clipping plane coordinate.
nearClip : float
Near clipping plane distance from viewer.
farClip : float
Far clipping plane distance from viewer.
out : ndarray, optional
Optional output array. Must be same `shape` and `dtype` as the expected
output if `out` was not specified.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray
4x4 projection matrix
See Also
--------
perspectiveProjectionMatrix : Compute a perspective projection matrix.
Notes
-----
* The returned matrix is row-major. Values are floats with 32-bits of
precision stored as a contiguous (C-order) array.
"""
if out is None:
dtype = np.float64 if dtype is None else np.dtype(dtype).type
else:
dtype = np.dtype(out.dtype).type
projMat = np.zeros((4, 4,), dtype=dtype) if out is None else out
if out is not None:
projMat.fill(0.0)
u = dtype(2.0)
projMat[0, 0] = u / (right - left)
projMat[1, 1] = u / (top - bottom)
projMat[2, 2] = -u / (farClip - nearClip)
projMat[0, 3] = -((right + left) / (right - left))
projMat[1, 3] = -((top + bottom) / (top - bottom))
projMat[2, 3] = -((farClip + nearClip) / (farClip - nearClip))
projMat[3, 3] = 1.0
return projMat
[docs]def perspectiveProjectionMatrix(left, right, bottom, top, nearClip=0.01,
farClip=100., out=None, dtype=None):
"""Compute an perspective projection matrix with provided frustum
parameters. The frustum can be asymmetric.
Parameters
----------
left : float
Left clipping plane coordinate.
right : float
Right clipping plane coordinate.
bottom : float
Bottom clipping plane coordinate.
top : float
Top clipping plane coordinate.
nearClip : float
Near clipping plane distance from viewer.
farClip : float
Far clipping plane distance from viewer.
out : ndarray, optional
Optional output array. Must be same `shape` and `dtype` as the expected
output if `out` was not specified.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray
4x4 projection matrix
See Also
--------
orthoProjectionMatrix : Compute a orthographic projection matrix.
Notes
-----
* The returned matrix is row-major. Values are floats with 32-bits of
precision stored as a contiguous (C-order) array.
"""
if out is None:
dtype = np.float64 if dtype is None else np.dtype(dtype).type
else:
dtype = np.dtype(out.dtype).type
projMat = np.zeros((4, 4,), dtype=dtype) if out is None else out
if out is not None:
projMat.fill(0.0)
u = dtype(2.0)
projMat[0, 0] = (u * nearClip) / (right - left)
projMat[1, 1] = (u * nearClip) / (top - bottom)
projMat[0, 2] = (right + left) / (right - left)
projMat[1, 2] = (top + bottom) / (top - bottom)
projMat[2, 2] = -(farClip + nearClip) / (farClip - nearClip)
projMat[3, 2] = -1.0
projMat[2, 3] = -(u * farClip * nearClip) / (farClip - nearClip)
return projMat
[docs]def lookAt(eyePos, centerPos, upVec=(0.0, 1.0, 0.0), out=None, dtype=None):
"""Create a transformation matrix to orient a view towards some point. Based
on the same algorithm as 'gluLookAt'. This does not generate a projection
matrix, but rather the matrix to transform the observer's view in the scene.
For more information see:
https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluLookAt.xml
Parameters
----------
eyePos : list of float or ndarray
Eye position in the scene.
centerPos : list of float or ndarray
Position of the object center in the scene.
upVec : list of float or ndarray, optional
Vector defining the up vector. Default is +Y is up.
out : ndarray, optional
Optional output array. Must be same `shape` and `dtype` as the expected
output if `out` was not specified.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray
4x4 view matrix
Notes
-----
* The returned matrix is row-major. Values are floats with 32-bits of
precision stored as a contiguous (C-order) array.
"""
if out is None:
dtype = np.float64 if dtype is None else np.dtype(dtype).type
else:
dtype = np.dtype(out.dtype).type
toReturn = np.zeros((4, 4,), dtype=dtype) if out is None else out
if out is not None:
toReturn.fill(0.0)
eyePos = np.asarray(eyePos, dtype=dtype)
centerPos = np.asarray(centerPos, dtype=dtype)
upVec = np.asarray(upVec, dtype=dtype)
f = centerPos - eyePos
f /= np.linalg.norm(f)
upVec /= np.linalg.norm(upVec)
s = np.cross(f, upVec)
u = np.cross(s / np.linalg.norm(s), f)
rotMat = np.zeros((4, 4), dtype=dtype)
rotMat[0, :3] = s
rotMat[1, :3] = u
rotMat[2, :3] = -f
rotMat[3, 3] = 1.0
transMat = np.identity(4, dtype=dtype)
transMat[:3, 3] = -eyePos
return np.matmul(rotMat, transMat, out=toReturn)
def viewMatrix(pos, ori=(0., 0., 0., -1.), out=None, dtype=None):
"""Get a view matrix from a pose.
A pose consists of a position coordinate [X, Y, Z, 1] and orientation
quaternion [X, Y, Z, W]. Assumes that the identity pose has a forward vector
pointing along the -Z axis and up vector along the +Y axis. The quaternion
for `ori` must be normalized.
Parameters
----------
pos : ndarray, tuple, or list of float
Position vector [x, y, z].
ori : tuple, list or ndarray of float
Orientation quaternion in form [x, y, z, w] where w is real and x, y, z
are imaginary components.
out : ndarray, optional
Optional output array. Must be same `shape` and `dtype` as the expected
output if `out` was not specified.
dtype : dtype or str, optional
Data type for computations can either be 'float32' or 'float64'. If
`out` is specified, the data type of `out` is used and this argument is
ignored. If `out` is not provided, 'float64' is used by default.
"""
if out is None:
dtype = np.float64 if dtype is None else np.dtype(dtype).type
else:
dtype = np.dtype(dtype).type
# convert if needed
pos = np.asarray(pos, dtype=dtype)
ori = np.asarray(ori, dtype=dtype)
axes = np.asarray(VEC_FWD_AND_UP, dtype=dtype) # convert to type
toReturn = np.zeros((4, 4), dtype=dtype) if out is None else out
# generate rotation matrix
b, c, d, a = ori[:]
vsqr = np.square(ori)
R = np.zeros((3, 3,), dtype=dtype)
u = dtype(2.0)
R[0, 0] = vsqr[3] + vsqr[0] - vsqr[1] - vsqr[2]
R[1, 0] = u * (b * c + a * d)
R[2, 0] = u * (b * d - a * c)
R[0, 1] = u * (b * c - a * d)
R[1, 1] = vsqr[3] - vsqr[0] + vsqr[1] - vsqr[2]
R[2, 1] = u * (c * d + a * b)
R[0, 2] = u * (b * d + a * c)
R[1, 2] = u * (c * d - a * b)
R[2, 2] = vsqr[3] - vsqr[0] - vsqr[1] + vsqr[2]
# transform the axes
transformedAxes = axes.dot(R.T)
fwdVec = transformedAxes[0, :] + pos
upVec = transformedAxes[1, :]
toReturn[:, :] = lookAt(pos, fwdVec, upVec, dtype=dtype)
return toReturn
[docs]def pointToNdc(wcsPos, viewMatrix, projectionMatrix, out=None, dtype=None):
"""Map the position of a point in world space to normalized device
coordinates/space.
Parameters
----------
wcsPos : tuple, list or ndarray
Nx3 position vector(s) (xyz) in world space coordinates.
viewMatrix : ndarray
4x4 view matrix.
projectionMatrix : ndarray
4x4 projection matrix.
out : ndarray, optional
Optional output array. Must be same `shape` and `dtype` as the expected
output if `out` was not specified.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray
3x1 vector of normalized device coordinates with type 'float32'
Notes
-----
* The point is not visible, falling outside of the viewing frustum, if the
returned coordinates fall outside of -1 and 1 along any dimension.
* In the rare instance the point falls directly on the eye in world
space where the frustum converges to a point (singularity), the divisor
will be zero during perspective division. To avoid this, the divisor is
'bumped' to 1e-5.
* This function assumes the display area is rectilinear. Any distortion or
warping applied in normalized device or viewport space is not considered.
Examples
--------
Determine if a point is visible::
point = (0.0, 0.0, 10.0) # behind the observer
ndc = pointToNdc(point, win.viewMatrix, win.projectionMatrix)
isVisible = not np.any((ndc > 1.0) | (ndc < -1.0))
Convert NDC to viewport (or pixel) coordinates::
scrRes = (1920, 1200)
point = (0.0, 0.0, -5.0) # forward -5.0 from eye
x, y, z = pointToNdc(point, win.viewMatrix, win.projectionMatrix)
pixelX = ((x + 1.0) / 2.0) * scrRes[0])
pixelY = ((y + 1.0) / 2.0) * scrRes[1])
# object at point will appear at (pixelX, pixelY)
"""
if out is None:
dtype = np.float64 if dtype is None else np.dtype(dtype).type
else:
dtype = np.dtype(out.dtype).type
wcsPos = np.asarray(wcsPos, dtype=dtype) # convert to array
toReturn = np.zeros_like(wcsPos, dtype=dtype) if out is None else out
# forward transform from world to clipping space
viewProjMatrix = np.zeros((4, 4,), dtype=dtype)
np.matmul(projectionMatrix, viewMatrix, viewProjMatrix)
pnts, rtn = np.atleast_2d(wcsPos, toReturn)
# convert to 4-vector with W=1.0
wcsVec = np.zeros((pnts.shape[0], 4), dtype=dtype)
wcsVec[:, :3] = wcsPos
wcsVec[:, 3] = 1.0
# convert to homogeneous clip space
wcsVec = mt.applyMatrix(viewProjMatrix, wcsVec, dtype=dtype)
# handle the singularity where perspective division will fail
wcsVec[np.abs(wcsVec[:, 3]) <= np.finfo(dtype).eps] = np.finfo(dtype).eps
rtn[:, :] = wcsVec[:, :3] / wcsVec[:, 3:] # xyz / w
return toReturn
[docs]def cursorToRay(cursorX, cursorY, winSize, viewport, projectionMatrix,
normalize=True, out=None, dtype=None):
"""Convert a 2D mouse coordinate to a 3D ray.
Takes a 2D window/mouse coordinate and transforms it to a 3D direction
vector from the viewpoint in eye space (vector origin is [0, 0, 0]). The
center of the screen projects to vector [0, 0, -1].
Parameters
----------
cursorX, cursorY : float or int
Window coordinates. These need to be scaled if you are using a
framebuffer that does not have 1:1 pixel mapping (i.e. retina display).
winSize : array_like
Size of the window client area [w, h].
viewport : array_like
Viewport rectangle [x, y, w, h] being used.
projectionMatrix : ndarray
4x4 projection matrix being used.
normalize : bool
Normalize the resulting vector.
out : ndarray, optional
Optional output array. Must be same `shape` and `dtype` as the expected
output if `out` was not specified.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray
Direction vector (x, y, z).
Examples
--------
Place a 3D stim at the mouse location 5.0 scene units (meters) away::
# define camera
camera = RigidBodyPose((-3.0, 5.0, 3.5))
camera.alignTo((0, 0, 0))
# in the render loop
dist = 5.0
mouseRay = vt.cursorToRay(x, y, win.size, win.viewport, win.projectionMatrix)
mouseRay *= dist # scale the vector
# set the sphere position by transforming vector to world space
sphere.thePose.pos = camera.transform(mouseRay)
"""
if out is None:
dtype = np.float64 if dtype is None else np.dtype(dtype).type
else:
dtype = np.dtype(out.dtype).type
toReturn = np.zeros((3,), dtype=dtype) if out is None else out
projectionMatrix = np.asarray(projectionMatrix, dtype=dtype)
# compute the inverse model/view and projection matrix
invPM = np.linalg.inv(projectionMatrix)
# transform psychopy mouse coordinates to viewport coordinates
cursorX = cursorX + (winSize[0] / 2.0)
cursorY = cursorY + (winSize[1] / 2.0)
# get the NDC coordinates of the
projX = 2. * (cursorX - viewport[0]) / viewport[2] - 1.0
projY = 2. * (cursorY - viewport[1]) / viewport[3] - 1.0
vecNear = np.array((projX, projY, 0.0, 1.0), dtype=dtype)
vecFar = np.array((projX, projY, 1.0, 1.0), dtype=dtype)
vecNear[:] = vecNear.dot(invPM.T)
vecFar[:] = vecFar.dot(invPM.T)
vecNear /= vecNear[3]
vecFar /= vecFar[3]
# direction vector
toReturn[:] = (vecFar - vecNear)[:3]
if normalize:
mt.normalize(toReturn, out=toReturn)
return toReturn
[docs]def visibleBBox(extents, mvp, dtype=None):
"""Check if a bounding box is visible.
This function checks if a bonding box intersects a frustum defined by the
current projection matrix, after being transformed by the model-view matrix.
Parameters
----------
extents : array_like
Bounding box minimum and maximum extents as a 2x3 array. The first row
if the minimum extents along each axis, and the second row the maximum
extents (eg. [[minX, minY, minZ], [maxX, maxY, maxZ]]).
mvp : array_like
4x4 MVP matrix.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
ndarray or bool
Visibility test results.
"""
dtype = np.float64 if dtype is None else np.dtype(dtype).type
# convert input if needed
extents = np.asarray(extents, dtype=dtype)
if not extents.shape == (2, 3):
raise ValueError("Invalid array dimensions for `extents`.")
# ensure matrix is array
mvp = np.asarray(mvp, dtype=dtype)
# convert BBox to corners
corners = mt.computeBBoxCorners(extents, dtype=dtype)
# apply the matrix
corners = corners.dot(mvp.T)
# break up into components
x, y, z = corners[:, 0], corners[:, 1], corners[:, 2]
wpos, wneg = corners[:, 3], -corners[:, 3]
# test if box falls all to one side of the frustum
if np.logical_xor(np.all(x <= wneg), np.all(x >= wpos)): # x-axis
return False
elif np.logical_xor(np.all(y <= wneg), np.all(y >= wpos)): # y-axis
return False
elif np.logical_xor(np.all(z <= wneg), np.all(z >= wpos)): # z-axis
return False
else:
return True
[docs]def visible(points, mvp, mode='discrete', dtype=None):
"""Test if points are visible.
This function is useful for visibility culling, where objects are only drawn
if a portion of them are visible. This test can avoid costly drawing calls
and OpenGL state changes if the object is not visible.
Parameters
----------
points : array_like
Point(s) or bounding box to test. Input array must be Nx3 or Nx4, where
each row is a point. It is recommended that the input be Nx4 since the
`w` component will be appended if the input is Nx3 which adds overhead.
mvp : array_like
4x4 MVP matrix.
mode : str
Test mode. If `'discrete'`, rows of `points` are treated as individual
points. This function will return an array of boolean values with length
equal to the number of rows in `points`, where the value at each index
corresponds to the visibility test results for points at the matching
row index of `points`. If `'group'` a single boolean value is returned,
which is `False` if all points fall to one side of the frustum.
dtype : dtype or str, optional
Data type for arrays, can either be 'float32' or 'float64'. If `None` is
specified, the data type is inferred by `out`. If `out` is not provided,
the default is 'float64'.
Returns
-------
bool or ndarray
Test results. The type returned depends on `mode`.
Examples
--------
Visibility culling, only a draw line connecting two points if visible::
linePoints = [[-1.0, -1.0, -1.0, 1.0],
[ 1.0, 1.0, 1.0, 1.0]]
mvp = np.matmul(win.projectionMatrix, win.viewMatrix)
if visible(linePoints, mvp, mode='group'):
# drawing commands here ...
"""
dtype = np.float64 if dtype is None else np.dtype(dtype).type
# convert input if needed
points = np.asarray(points, dtype=dtype)
# keep track of dimension, return only a single value if ndim==1
ndim = points.ndim
# ensure matrix is array
mvp = np.asarray(mvp, dtype=dtype)
# convert to 2d view
points = np.atleast_2d(np.asarray(points, dtype=dtype))
if points.shape[1] == 3: # make sure we are using Nx4
temp = np.zeros((points.shape[0], 4), dtype=dtype)
temp[:, :3] = points
temp[:, 3] = 1.0
points = temp
# apply the matrix
points = points.dot(mvp.T)
# break up into components
x, y, z = points[:, 0], points[:, 1], points[:, 2]
wpos, wneg = points[:, 3], -points[:, 3]
# test using the appropriate mode
if mode == 'discrete':
toReturn = np.logical_and.reduce(
(x > wneg, x < wpos, y > wneg, y < wpos, z > wneg, z < wpos))
return toReturn[0] if ndim == 1 else toReturn
elif mode == 'group':
# Check conditions for each axis. If all points fall to one side or
# another, the bounding box is not visible. If all points fall outside
# of both sides of the frustum along the same axis, that means the box
# passes through the frustum or the viewer is inside the bounding box
# and therefore is visible. We do an XOR to capture conditions where all
# points fall all to one side only. Lastly, if any point is in the
# bounding box, it will indicate that it's visible.
#
# mdc - This has been vectorized to be super fast, however maybe someone
# smarter than me can figure out something better.
#
if np.logical_xor(np.all(x <= wneg), np.all(x >= wpos)): # x-axis
return False
elif np.logical_xor(np.all(y <= wneg), np.all(y >= wpos)): # y-axis
return False
elif np.logical_xor(np.all(z <= wneg), np.all(z >= wpos)): # z-axis
return False
else:
return True
else:
raise ValueError(
"Invalid `mode` specified, should be either 'discrete' or 'group'.")
