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# -*- coding: utf-8 -*-
# vispy: gallery 30
# -----------------------------------------------------------------------------
# Copyright (c) Vispy Development Team. All Rights Reserved.
# Distributed under the (new) BSD License. See LICENSE.txt for more info.
# -----------------------------------------------------------------------------
# Author: John David Reaver
# Date: 09/12/2014
# -----------------------------------------------------------------------------
"""
Example demonstrating the use of emulated double-precision floating point
numbers. Based off of mandelbrot.py.
The shader program emulates double-precision variables using a vec2 instead of
single-precision floats. Any function starting with ds_* operates on these
variables. See http://www.thasler.org/blog/?p=93.
NOTE: Some NVIDIA cards optimize the double-precision code away. Results are
therefore hardware dependent.
"""
from __future__ import division
import numpy as np
from vispy import app, gloo
# Shader source code
# -----------------------------------------------------------------------------
vertex = """
attribute vec2 position;
void main()
{
gl_Position = vec4(position, 0, 1.0);
}
"""
fragment = """
#pragma optionNV(fastmath off)
#pragma optionNV(fastprecision off)
uniform vec2 inv_resolution_x; // Inverse resolutions
uniform vec2 inv_resolution_y;
uniform vec2 center_x;
uniform vec2 center_y;
uniform vec2 scale;
uniform int iter;
// Jet color scheme
vec4 color_scheme(float x) {
vec3 a, b;
float c;
if (x < 0.34) {
a = vec3(0, 0, 0.5);
b = vec3(0, 0.8, 0.95);
c = (x - 0.0) / (0.34 - 0.0);
} else if (x < 0.64) {
a = vec3(0, 0.8, 0.95);
b = vec3(0.85, 1, 0.04);
c = (x - 0.34) / (0.64 - 0.34);
} else if (x < 0.89) {
a = vec3(0.85, 1, 0.04);
b = vec3(0.96, 0.7, 0);
c = (x - 0.64) / (0.89 - 0.64);
} else {
a = vec3(0.96, 0.7, 0);
b = vec3(0.5, 0, 0);
c = (x - 0.89) / (1.0 - 0.89);
}
return vec4(mix(a, b, c), 1.0);
}
vec2 ds_set(float a) {
// Create an emulated double by storing first part of float in first half
// of vec2
vec2 z;
z.x = a;
z.y = 0.0;
return z;
}
vec2 ds_add (vec2 dsa, vec2 dsb)
{
// Add two emulated doubles. Complexity comes from carry-over.
vec2 dsc;
float t1, t2, e;
t1 = dsa.x + dsb.x;
e = t1 - dsa.x;
t2 = ((dsb.x - e) + (dsa.x - (t1 - e))) + dsa.y + dsb.y;
dsc.x = t1 + t2;
dsc.y = t2 - (dsc.x - t1);
return dsc;
}
vec2 ds_mul (vec2 dsa, vec2 dsb)
{
vec2 dsc;
float c11, c21, c2, e, t1, t2;
float a1, a2, b1, b2, cona, conb, split = 8193.;
cona = dsa.x * split;
conb = dsb.x * split;
a1 = cona - (cona - dsa.x);
b1 = conb - (conb - dsb.x);
a2 = dsa.x - a1;
b2 = dsb.x - b1;
c11 = dsa.x * dsb.x;
c21 = a2 * b2 + (a2 * b1 + (a1 * b2 + (a1 * b1 - c11)));
c2 = dsa.x * dsb.y + dsa.y * dsb.x;
t1 = c11 + c2;
e = t1 - c11;
t2 = dsa.y * dsb.y + ((c2 - e) + (c11 - (t1 - e))) + c21;
dsc.x = t1 + t2;
dsc.y = t2 - (dsc.x - t1);
return dsc;
}
// Compare: res = -1 if a < b
// = 0 if a == b
// = 1 if a > b
float ds_compare(vec2 dsa, vec2 dsb)
{
if (dsa.x < dsb.x) return -1.;
else if (dsa.x == dsb.x) {
if (dsa.y < dsb.y) return -1.;
else if (dsa.y == dsb.y) return 0.;
else return 1.;
}
else return 1.;
}
void main() {
vec2 z_x, z_y, c_x, c_y, x, y, frag_x, frag_y;
vec2 four = ds_set(4.0);
vec2 point5 = ds_set(0.5);
// Recover coordinates from pixel coordinates
frag_x = ds_set(gl_FragCoord.x);
frag_y = ds_set(gl_FragCoord.y);
c_x = ds_add(ds_mul(frag_x, inv_resolution_x), -point5);
c_x = ds_add(ds_mul(c_x, scale), center_x);
c_y = ds_add(ds_mul(frag_y, inv_resolution_y), -point5);
c_y = ds_add(ds_mul(c_y, scale), center_y);
// Main Mandelbrot computation
int i;
z_x = c_x;
z_y = c_y;
for(i = 0; i < iter; i++) {
x = ds_add(ds_add(ds_mul(z_x, z_x), -ds_mul(z_y, z_y)), c_x);
y = ds_add(ds_add(ds_mul(z_y, z_x), ds_mul(z_x, z_y)), c_y);
if(ds_compare(ds_add(ds_mul(x, x), ds_mul(y, y)), four) > 0.) break;
z_x = x;
z_y = y;
}
// Convert iterations to color
float color = 1.0 - float(i) / float(iter);
gl_FragColor = color_scheme(color);
}
"""
# vispy Canvas
# -----------------------------------------------------------------------------
class Canvas(app.Canvas):
def __init__(self, *args, **kwargs):
app.Canvas.__init__(self, *args, **kwargs)
self.program = gloo.Program(vertex, fragment)
# Draw a rectangle that takes up the whole screen. All of the work is
# done in the shader.
self.program["position"] = [(-1, -1), (-1, 1), (1, 1),
(-1, -1), (1, 1), (1, -1)]
self.scale = 3
self.program["scale"] = set_emulated_double(self.scale)
self.center = [-0.5, 0]
self.bounds = [-2, 2]
self.translate_center(0, 0)
self.iterations = self.program["iter"] = 300
self.apply_zoom()
self.min_scale = 1e-12
self.max_scale = 4
gloo.set_clear_color(color='black')
self.show()
def on_draw(self, event):
self.program.draw()
def on_resize(self, event):
self.apply_zoom()
def apply_zoom(self):
width, height = self.physical_size
gloo.set_viewport(0, 0, width, height)
self.program['inv_resolution_x'] = set_emulated_double(1 / width)
self.program['inv_resolution_y'] = set_emulated_double(1 / height)
def on_mouse_move(self, event):
"""Pan the view based on the change in mouse position."""
if event.is_dragging and event.buttons[0] == 1:
x0, y0 = event.last_event.pos[0], event.last_event.pos[1]
x1, y1 = event.pos[0], event.pos[1]
X0, Y0 = self.pixel_to_coords(float(x0), float(y0))
X1, Y1 = self.pixel_to_coords(float(x1), float(y1))
self.translate_center(X1 - X0, Y1 - Y0)
self.update()
def translate_center(self, dx, dy):
"""Translates the center point, and keeps it in bounds."""
center = self.center
center[0] -= dx
center[1] -= dy
center[0] = min(max(center[0], self.bounds[0]), self.bounds[1])
center[1] = min(max(center[1], self.bounds[0]), self.bounds[1])
self.center = center
center_x = set_emulated_double(center[0])
center_y = set_emulated_double(center[1])
self.program["center_x"] = center_x
self.program["center_y"] = center_y
def pixel_to_coords(self, x, y):
"""Convert pixel coordinates to Mandelbrot set coordinates."""
rx, ry = self.size
nx = (x / rx - 0.5) * self.scale + self.center[0]
ny = ((ry - y) / ry - 0.5) * self.scale + self.center[1]
return [nx, ny]
def on_mouse_wheel(self, event):
"""Use the mouse wheel to zoom."""
delta = event.delta[1]
if delta > 0: # Zoom in
factor = 0.9
elif delta < 0: # Zoom out
factor = 1 / 0.9
for _ in range(int(abs(delta))):
self.zoom(factor, event.pos)
self.update()
def on_key_press(self, event):
"""Use + or - to zoom in and out.
The mouse wheel can be used to zoom, but some people don't have mouse
wheels :)
"""
if event.text == '+' or event.text == '=':
self.zoom(0.9)
elif event.text == '-':
self.zoom(1/0.9)
self.update()
def zoom(self, factor, mouse_coords=None):
"""Factors less than zero zoom in, and greater than zero zoom out.
If mouse_coords is given, the point under the mouse stays stationary
while zooming. mouse_coords should come from MouseEvent.pos.
"""
if mouse_coords is not None: # Record the position of the mouse
x, y = float(mouse_coords[0]), float(mouse_coords[1])
x0, y0 = self.pixel_to_coords(x, y)
self.scale *= factor
self.scale = max(min(self.scale, self.max_scale), self.min_scale)
self.program["scale"] = set_emulated_double(self.scale)
if mouse_coords is not None: # Translate so mouse point is stationary
x1, y1 = self.pixel_to_coords(x, y)
self.translate_center(x1 - x0, y1 - y0)
def set_emulated_double(number):
"""Emulate a double using two numbers of type float32."""
double = np.array([number, 0], dtype=np.float32) # Cast number to float32
double[1] = number - double[0] # Remainder stored in second half of array
return double
if __name__ == '__main__':
canvas = Canvas(size=(800, 800), keys='interactive')
app.run()
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