Source code for psychopy.tools.viewtools

#!/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) 2019-2021 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'.")

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