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# -*- coding: utf-8 -*-
# Copyright (c) Vispy Development Team. All Rights Reserved.
# Distributed under the (new) BSD License. See LICENSE.txt for more info.
from __future__ import division
import numpy as np
from ._util import arg_to_array, arg_to_vec4, as_vec4
from .base_transform import BaseTransform
from ... import gloo
class LogTransform(BaseTransform):
""" Transform perfoming logarithmic transformation on three axes.
Maps (x, y, z) => (log(base.x, x), log(base.y, y), log(base.z, z))
No transformation is applied for axes with base == 0.
If base < 0, then the inverse function is applied: x => base.x ** x
Parameters
----------
base : array-like
Base for the X, Y, Z axes.
"""
# TODO: Evaluate the performance costs of using conditionals.
# An alternative approach is to transpose the vector before
# log-transforming, and then transpose back afterward.
glsl_map = """
vec4 LogTransform_map(vec4 pos) {
if($base.x > 1.0)
pos.x = log(pos.x) / log($base.x);
else if($base.x < -1.0)
pos.x = pow(-$base.x, pos.x);
if($base.y > 1.0)
pos.y = log(pos.y) / log($base.y);
else if($base.y < -1.0)
pos.y = pow(-$base.y, pos.y);
if($base.z > 1.0)
pos.z = log(pos.z) / log($base.z);
else if($base.z < -1.0)
pos.z = pow(-$base.z, pos.z);
return pos;
}
"""
glsl_imap = glsl_map
Linear = False
Orthogonal = True
NonScaling = False
Isometric = False
def __init__(self, base=None):
super(LogTransform, self).__init__()
self._base = np.zeros(3, dtype=np.float32)
self.base = (0.0, 0.0, 0.0) if base is None else base
@property
def base(self):
"""
*base* is a tuple (x, y, z) containing the log base that should be
applied to each axis of the input vector. If any axis has a base <= 0,
then that axis is not affected.
"""
return self._base.copy()
@base.setter
def base(self, s):
self._base[:len(s)] = s
self._base[len(s):] = 0.0
@arg_to_array
def map(self, coords, base=None):
ret = np.empty(coords.shape, coords.dtype)
if base is None:
base = self.base
for i in range(min(ret.shape[-1], 3)):
if base[i] > 1.0:
ret[..., i] = np.log(coords[..., i]) / np.log(base[i])
elif base[i] < -1.0:
ret[..., i] = -base[i] ** coords[..., i]
else:
ret[..., i] = coords[..., i]
return ret
@arg_to_array
def imap(self, coords):
return self.map(coords, -self.base)
def shader_map(self):
fn = super(LogTransform, self).shader_map()
fn['base'] = self.base # uniform vec3
return fn
def shader_imap(self):
fn = super(LogTransform, self).shader_imap()
fn['base'] = -self.base # uniform vec3
return fn
def __repr__(self):
return "<LogTransform base=%s>" % (self.base)
class PolarTransform(BaseTransform):
"""Polar transform
Maps (theta, r, z) to (x, y, z), where `x = r*cos(theta)`
and `y = r*sin(theta)`.
"""
glsl_map = """
vec4 polar_transform_map(vec4 pos) {
return vec4(pos.y * cos(pos.x), pos.y * sin(pos.x), pos.z, 1);
}
"""
glsl_imap = """
vec4 polar_transform_map(vec4 pos) {
// TODO: need some modulo math to handle larger theta values..?
float theta = atan(pos.y, pos.x);
float r = length(pos.xy);
return vec4(theta, r, pos.z, 1);
}
"""
Linear = False
Orthogonal = False
NonScaling = False
Isometric = False
@arg_to_array
def map(self, coords):
ret = np.empty(coords.shape, coords.dtype)
ret[..., 0] = coords[..., 1] * np.cos(coords[..., 0])
ret[..., 1] = coords[..., 1] * np.sin(coords[..., 0])
for i in range(2, coords.shape[-1]): # copy any further axes
ret[..., i] = coords[..., i]
return ret
@arg_to_array
def imap(self, coords):
ret = np.empty(coords.shape, coords.dtype)
ret[..., 0] = np.arctan2(coords[..., 0], coords[..., 1])
ret[..., 1] = (coords[..., 0]**2 + coords[..., 1]**2) ** 0.5
for i in range(2, coords.shape[-1]): # copy any further axes
ret[..., i] = coords[..., i]
return ret
#class BilinearTransform(BaseTransform):
# # TODO
# pass
#class WarpTransform(BaseTransform):
# """ Multiple bilinear transforms in a grid arrangement.
# """
# # TODO
class MagnifyTransform(BaseTransform):
""" Magnifying lens transform.
This transform causes a circular region to appear with larger scale around
its center point.
Parameters
----------
mag : float
Magnification factor. Objects around the transform's center point will
appear scaled by this amount relative to objects outside the circle.
radii : (float, float)
Inner and outer radii of the "lens". Objects inside the inner radius
appear scaled, whereas objects outside the outer radius are unscaled,
and the scale factor transitions smoothly between the two radii.
center: (float, float)
The center (x, y) point of the "lens".
Notes
-----
This transform works by segmenting its input coordinates into three
regions--inner, outer, and transition. Coordinates in the inner region are
multiplied by a constant scale factor around the center point, and
coordinates in the transition region are scaled by a factor that
transitions smoothly from the inner radius to the outer radius.
Smooth functions that are appropriate for the transition region also tend
to be difficult to invert analytically, so this transform instead samples
the function numerically to allow trivial inversion. In OpenGL, the
sampling is implemented as a texture holding a lookup table.
"""
glsl_map = """
vec4 mag_transform(vec4 pos) {
vec2 d = vec2(pos.x - $center.x, pos.y - $center.y);
float dist = length(d);
if (dist == 0 || dist > $radii.y || ($mag < 1.01 && $mag > 0.99)) {
return pos;
}
vec2 dir = d / dist;
if( dist < $radii.x ) {
dist = dist * $mag;
}
else {
float r1 = $radii.x;
float r2 = $radii.y;
float x = (dist - r1) / (r2 - r1);
float s = texture2D($trans, vec2(0, x)).r * $trans_max;
dist = s;
}
d = $center + dir * dist;
return vec4(d, pos.z, pos.w);
}"""
glsl_imap = glsl_map
Linear = False
_trans_resolution = 1000
def __init__(self, mag=3, radii=(7, 10), center=(0, 0)):
self._center = center
self._mag = mag
self._radii = radii
self._trans = None
res = self._trans_resolution
self._trans_tex = (gloo.Texture2D((res, 1, 1), interpolation='linear'),
gloo.Texture2D((res, 1, 1), interpolation='linear'))
self._trans_tex_max = None
super(MagnifyTransform, self).__init__()
@property
def center(self):
""" The (x, y) center point of the transform.
"""
return self._center
@center.setter
def center(self, center):
if np.allclose(self._center, center):
return
self._center = center
self.shader_map()
self.shader_imap()
@property
def mag(self):
""" The scale factor used in the central region of the transform.
"""
return self._mag
@mag.setter
def mag(self, mag):
if self._mag == mag:
return
self._mag = mag
self._trans = None
self.shader_map()
self.shader_imap()
@property
def radii(self):
""" The inner and outer radii of the circular area bounding the
transform.
"""
return self._radii
@radii.setter
def radii(self, radii):
if np.allclose(self._radii, radii):
return
self._radii = radii
self._trans = None
self.shader_map()
self.shader_imap()
def shader_map(self):
fn = super(MagnifyTransform, self).shader_map()
fn['center'] = self._center # uniform vec2
fn['mag'] = self._mag
fn['radii'] = (self._radii[0] / self._mag, self._radii[1])
self._get_transition() # make sure transition texture is up to date
fn['trans'] = self._trans_tex[0]
fn['trans_max'] = self._trans_tex_max[0]
return fn
def shader_imap(self):
fn = super(MagnifyTransform, self).shader_imap()
fn['center'] = self._center # uniform vec2
fn['mag'] = 1. / self._mag
fn['radii'] = self._radii
self._get_transition() # make sure transition texture is up to date
fn['trans'] = self._trans_tex[1]
fn['trans_max'] = self._trans_tex_max[1]
return fn
@arg_to_vec4
def map(self, x, _inverse=False):
c = as_vec4(self.center)[0]
m = self.mag
r1, r2 = self.radii
xm = np.empty(x.shape, dtype=x.dtype)
dx = (x - c)
dist = (((dx**2).sum(axis=-1)) ** 0.5)[..., np.newaxis]
dist[np.isnan(dist)] = 0
unit = dx / np.where(dist != 0, dist, 1)
# magnified center region
if _inverse:
inner = (dist < r1)[:, 0]
s = dist / m
else:
inner = (dist < (r1 / m))[:, 0]
s = dist * m
xm[inner] = c + unit[inner] * s[inner]
# unmagnified outer region
outer = (dist > r2)[:, 0]
xm[outer] = x[outer]
# smooth transition region, interpolated from trans
trans = ~(inner | outer)
# look up scale factor from trans
temp, itemp = self._get_transition()
if _inverse:
tind = (dist[trans] - r1) * len(itemp) / (r2 - r1)
temp = itemp
else:
tind = (dist[trans] - (r1/m)) * len(temp) / (r2 - (r1/m))
tind = np.clip(tind, 0, temp.shape[0]-1)
s = temp[tind.astype(int)]
xm[trans] = c + unit[trans] * s
return xm
def imap(self, coords):
return self.map(coords, _inverse=True)
def _get_transition(self):
# Generate forward/reverse transition templates.
# We would prefer to express this with an invertible function, but that
# turns out to be tricky. The templates make any function invertible.
if self._trans is None:
m, r1, r2 = self.mag, self.radii[0], self.radii[1]
res = self._trans_resolution
xi = np.linspace(r1, r2, res)
t = 0.5 * (1 + np.cos((xi - r2) * np.pi / (r2 - r1)))
yi = (xi * t + xi * (1-t) / m).astype(np.float32)
x = np.linspace(r1 / m, r2, res)
y = np.interp(x, yi, xi).astype(np.float32)
self._trans = (y, yi)
# scale to 0.0-1.0 to prevent clipping (is this necessary?)
mx = y.max(), yi.max()
self._trans_tex_max = mx
self._trans_tex[0].set_data((y/mx[0])[:, np.newaxis, np.newaxis])
self._trans_tex[1].set_data((yi/mx[1])[:, np.newaxis, np.newaxis])
return self._trans
class Magnify1DTransform(MagnifyTransform):
""" A 1-dimensional analog of MagnifyTransform. This transform expands
its input along the x-axis, around a center x value.
"""
glsl_map = """
vec4 mag_transform(vec4 pos) {
float dist = pos.x - $center.x;
if (dist == 0 || abs(dist) > $radii.y || $mag == 1) {
return pos;
}
float dir = dist / abs(dist);
if( abs(dist) < $radii.x ) {
dist = dist * $mag;
}
else {
float r1 = $radii.x;
float r2 = $radii.y;
float x = (abs(dist) - r1) / (r2 - r1);
dist = dir * texture2D($trans, vec2(0, x)).r * $trans_max;
}
return vec4($center.x + dist, pos.y, pos.z, pos.w);
}"""
glsl_imap = glsl_map