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LICENSE
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The MIT License (MIT)
Copyright (c) 2014 Michele Guerini Rocco
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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README.md
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terrain
=======
# Terrain
Simple terrain generator
## Simple terrain generator
![Screenshot](screenshot.png)
## Info
A simple application which uses the diamond square algorithm to generate a terrain and renders it in OpenGL.
### License
Dual licensed under the MIT and GPL licenses:
http://www.opensource.org/licenses/mit-license.php
http://www.gnu.org/licenses/gpl.html

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terrain.py Normal file
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import random
import numpy
import pyglet
from pyglet.gl import *
from trackball_camera import TrackballCamera
class Terrain():
def __init__(self, details):
self.size = 2 ** details + 1
self.map = numpy.zeros((self.size, self.size))
def _square(self, x, y, size, offset):
average = sum([
self.map[x - size][y - size],
self.map[x + size][y - size],
self.map[x + size][y + size],
self.map[x - size][y + size]]) / 4
self.map[x][y] = average + offset
def _diamond(self, x, y, size, offset):
average = sum([
self.map[x][y - size],
self.map[x + size][y],
self.map[x][y + size],
self.map[x - size][y]]) / 4
self.map[x][y] = average + offset
def generate(self, high):
i, half = self.size - 1, (self.size - 1) / 2
scale = high * self.size
while i > 1:
for y in numpy.arange(half, self.size - 1, i):
for x in numpy.arange(half, self.size - 1, i):
self._square(x, y, half, scale / 2 * random.random())
for y in numpy.arange(0, self.size - 1, half):
for x in numpy.arange((y + half) % i, self.size - 1, i):
self._diamond(x, y, half, scale / 2 * random.random())
i /= 2
half = i / 2
scale = high * half * 2
class Window(pyglet.window.Window):
def __init__(self, *args, **kwargs):
self.terrain = None
self.camera = kwargs['camera']
del kwargs['camera']
super().__init__(*args, **kwargs)
# Initialize OpenGL
glEnable(GL_DEPTH_TEST)
glDisable(GL_CULL_FACE)
def on_mouse_drag(self, x, y, dx, dy, buttons, modifiers):
"""Move camera/zoom on mouse drag"""
if buttons & pyglet.window.mouse.LEFT:
self.camera.mouse_roll(
self._norm(x, self.width),
self._norm(y, self.height))
elif buttons & pyglet.window.mouse.RIGHT:
self.camera.mouse_zoom(
self._norm(x * 2, self.width),
self._norm(y * 2, self.height))
def on_mouse_press(self, x, y, button, modifiers):
"""Move camera/zoom on mouse drag"""
if button == pyglet.window.mouse.LEFT:
self.camera.mouse_roll(
self._norm(x, self.width),
self._norm(y, self.height),
False)
elif button == pyglet.window.mouse.RIGHT:
self.camera.mouse_zoom(
self._norm(x * 2, self.width),
self._norm(y * 2, self.height),
False)
def on_resize(self, width, height):
"""Adjust drawing after window is resized"""
self.width = width
self.height = height
glViewport(0, 0, self.width, self.height)
self.on_show()
def on_show(self):
"""Set OpenGl config"""
glMatrixMode(GL_PROJECTION)
glLoadIdentity()
gluPerspective(40, self.width / self.height, 1, 400)
self.camera.update_modelview()
def on_draw(self):
"""Draw the current frame"""
if self.terrain is None:
return
self.clear()
map, size = self.terrain.map, self.terrain.size
glPushMatrix()
glTranslatef(-size / 2, 0, -size / 2)
# Draw terrain
for x in numpy.arange(size - 1):
for y in numpy.arange(size - 1):
glBegin(GL_TRIANGLE_STRIP)
glColor3f(map[x][y] / 20, map[x][y] / 20, map[x][y] / 20)
glVertex3f(x, map[x][y], y)
glVertex3f(x + 1, map[x + 1][y], y)
glVertex3f(x, map[x][y + 1], y + 1)
glVertex3f(x + 1, map[x + 1][y + 1], y + 1)
glEnd()
glPopMatrix()
# Draw axis
glBegin(GL_LINES)
glColor3f(1, 0, 0)
glVertex3f(-size, 0, 0)
glVertex3f(size, 0, 0)
glColor3f(0, 1, 0)
glVertex3f(0, -size, 0)
glVertex3f(0, size, 0)
glColor3f(0, 0, 1)
glVertex3f(0, 0, -size)
glVertex3f(0, 0, size)
glEnd()
def _norm(self, x, max_x):
"""given x within [0,max_x], scale to a range [-1,1]"""
return (2 * x - float(max_x)) / float(max_x)
def draw(self, terrain):
"""Render the height map"""
self.terrain = terrain
def main():
terrain = Terrain(5)
camera = TrackballCamera(150)
window = Window(caption="Terrain", resizable=True,
width=800, height=600, camera=camera)
terrain.generate(0.7)
window.draw(terrain)
pyglet.app.run()
if __name__ == '__main__':
main()

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"""trackball_camera.py - An OpenGL Trackball Camera Class for Pyglet
by Roger Allen, July 2008
roger@rogerandwendy.com
A class for simple-minded 3d example apps.
Usage:
Initialize with a radius from the center/focus point:
tbcam = TrackballCamera(5.0)
After adjusting your projection matrix, set the modelview matrix.
tbcam.update_modelview()
On each primary mouse click, scale the x & y to [-1,1] and call:
tbcam.mouse_roll(x,y,False)
On each primary mouse drag, scale the x & y to [-1,1] and call:
tbcam.mouse_roll(x,y)
Mouse movements adjust the modelview projection matrix directly.
"""
__version__ = "1.0"
# Code derived from the GLUT trackball.c, but now quite different and
# customized for pyglet.
#
# I simply wanted an easy-to-use trackball camera for quick-n-dirty
# opengl programs that I'd like to write. Finding none, I grabbed
# the trackball.c code & started hacking.
#
# Originally implemented by Gavin Bell, lots of ideas from Thant Tessman
# and the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
# and David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
#
# Note: See the following for more information on quaternions:
#
# - Shoemake, K., Animating rotation with quaternion curves, Computer
# Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
# - Pletinckx, D., Quaternion calculus as a basic tool in computer
# graphics, The Visual Computer 5, 2-13, 1989.
#
# Gavin Bell's code had this copyright notice:
# (c) Copyright 1993, 1994, Silicon Graphics, Inc.
# ALL RIGHTS RESERVED
# Permission to use, copy, modify, and distribute this software for
# any purpose and without fee is hereby granted, provided that the above
# copyright notice appear in all copies and that both the copyright notice
# and this permission notice appear in supporting documentation, and that
# the name of Silicon Graphics, Inc. not be used in advertising
# or publicity pertaining to distribution of the software without specific,
# written prior permission.
#
# THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
# AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
# INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
# FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON
# GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
# SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
# KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
# LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
# THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN
# ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
# ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
# POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
#
# US Government Users Restricted Rights
# Use, duplication, or disclosure by the Government is subject to
# restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
# (c)(1)(ii) of the Rights in Technical Data and Computer Software
# clause at DFARS 252.227-7013 and/or in similar or successor
# clauses in the FAR or the DOD or NASA FAR Supplement.
# Unpublished-- rights reserved under the copyright laws of the
# United States. Contractor/manufacturer is Silicon Graphics,
# Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311.
import math
import copy
from pyglet.gl import *
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# a little vector library that is misused in odd ways below.
def v3add(src1, src2):
return [ src1[0] + src2[0],
src1[1] + src2[1],
src1[2] + src2[2] ]
def v3sub(src1, src2):
return [ src1[0] - src2[0],
src1[1] - src2[1],
src1[2] - src2[2] ]
def v3scale(v, scale):
return [ v[0] * scale,
v[1] * scale,
v[2] * scale ]
def v3dot(v1, v2):
return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]
def v3cross(v1, v2):
return [ (v1[1] * v2[2]) - (v1[2] * v2[1]),
(v1[2] * v2[0]) - (v1[0] * v2[2]),
(v1[0] * v2[1]) - (v1[1] * v2[0]) ]
def v3length(v):
return math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2])
def v3normalize(v):
try:
tmp = v3scale(v,1.0/v3length(v))
return tmp
except ZeroDivisionError:
return v
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Some quaternion routines
def q_add(q1, q2):
"""Given two quaternions, add them together to get a third quaternion.
Adding quaternions to get a compound rotation is analagous to adding
translations to get a compound translation. When incrementally
adding rotations, the first argument here should be the new rotation.
"""
t1 = v3scale(q1,q2[3])
t2 = v3scale(q2,q1[3])
t3 = v3cross(q2,q1)
tf = v3add(t1,t2)
tf = v3add(t3,tf)
tf.append( q1[3] * q2[3] - v3dot(q1,q2) )
return tf
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def q_from_axis_angle(a, phi):
# a is a 3-vector, q is a 4-vector
"""Computes a quaternion based on an axis (defined by the given vector)
and an angle about which to rotate. The angle is expressed in radians.
"""
q = v3normalize(a)
q = v3scale(q, math.sin(phi/2.0))
q.append(math.cos(phi/2.0))
return q
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def q_normalize(q):
"""Return a normalized quaternion"""
mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3])
if mag != 0:
for i in range(4):
q[i] /= mag;
return q
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def q_matrix(q):
"""return the rotation matrix based on q"""
m = [0.0]*16
m[0*4+0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2])
m[0*4+1] = 2.0 * (q[0] * q[1] - q[2] * q[3])
m[0*4+2] = 2.0 * (q[2] * q[0] + q[1] * q[3])
m[0*4+3] = 0.0
m[1*4+0] = 2.0 * (q[0] * q[1] + q[2] * q[3])
m[1*4+1] = 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0])
m[1*4+2] = 2.0 * (q[1] * q[2] - q[0] * q[3])
m[1*4+3] = 0.0
m[2*4+0] = 2.0 * (q[2] * q[0] - q[1] * q[3])
m[2*4+1] = 2.0 * (q[1] * q[2] + q[0] * q[3])
m[2*4+2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0])
m[2*4+3] = 0.0
m[3*4+0] = 0.0
m[3*4+1] = 0.0
m[3*4+2] = 0.0
m[3*4+3] = 1.0
return m
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def project_z(r, x, y):
"""Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
if we are away from the center of the sphere.
"""
d = math.sqrt(x*x + y*y)
if (d < r * 0.70710678118654752440): # Inside sphere
z = math.sqrt(r*r - d*d)
else: # On hyperbola
t = r / 1.41421356237309504880
z = t*t / d
return z
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# Trackball Camera Class
#
class TrackballCamera:
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def __init__(self, radius=1.0):
""" initialize the camera, giving a radius from the focal point for
the camera eye. Update focal point & up via the update_modelview call.
"""
# the quaternion storing the rotation
self.rot_quat = [0,0,0,1]
# the last mouse update
self.last_x = None
self.last_y = None
# camera vars
self.cam_eye = [0.,0.,radius]
self.cam_focus = [0.,0.,0.]
self.cam_up = [0.,1.,0.]
# in add_quat routine, renormalize "sometimes"
self.RENORMCOUNT = 97
self.count = 0
# Trackballsize should really be based on the distance from the center of
# rotation to the point on the object underneath the mouse. That
# point would then track the mouse as closely as possible. This is a
# simple example, though, so that is left as an Exercise for the
# Programmer.
self.TRACKBALLSIZE = 0.8
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def mouse_roll(self, norm_mouse_x, norm_mouse_y, dragging=True):
"""When you click or drag the primary mouse button, scale the mouse
x & y to the range [-1.0,1.0] and call this routine to roll the trackball
and update the modelview matrix.
The initial click should set dragging to False.
"""
if dragging:
norm_mouse_quat = self._rotate(norm_mouse_x, norm_mouse_y)
self.rot_quat = q_add(norm_mouse_quat,self.rot_quat)
self.count += 1
if (self.count > self.RENORMCOUNT):
self.rot_quat = q_normalize(self.rot_quat)
self.count = 0
self.update_modelview()
self.last_x = norm_mouse_x
self.last_y = norm_mouse_y
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def mouse_zoom(self, norm_mouse_x, norm_mouse_y, dragging=True):
"""When you click or drag a secondary mouse button, scale the mouse
x & y to the range [-1.0,1.0] and call this routine to change the
trackball's camera radius and update the modelview matrix.
The initial click should set dragging to False.
"""
if self.last_x:
dx = norm_mouse_x - self.last_x
dy = norm_mouse_y - self.last_y
norm_mouse_r_delta = 20.0*math.sqrt(dx*dx+dy*dy)
if dy > 0.0:
norm_mouse_r_delta = -norm_mouse_r_delta
if dragging:
self.cam_eye[2] = self.cam_eye[2] + norm_mouse_r_delta
if self.cam_eye[2] < 1.0:
self.cam_eye[2] == 1.0
self.update_modelview()
self.last_x = norm_mouse_x
self.last_y = norm_mouse_y
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def update_modelview(self,cam_radius=None,cam_focus=None,cam_up=None):
"""Given a radius for the trackball camera, a focus-point 3-vector,
another 3-vector the points 'up' combined with the current
orientation of the trackball, update the GL_MODELVIEW matrix.
"""
if cam_radius:
self.cam_eye[2] = cam_radius
if cam_focus:
self.cam_focus = cam_focus
if cam_up:
self.cam_up = cam_up
glMatrixMode(GL_MODELVIEW)
glLoadIdentity()
gluLookAt(
self.cam_eye[0],self.cam_eye[1],self.cam_eye[2],
self.cam_focus[0],self.cam_focus[1],self.cam_focus[2],
self.cam_up[0],self.cam_up[1],self.cam_up[2]
)
# rotate this view by the current orientation
m = self._matrix()
mm = (GLfloat * len(m))(*m) # FIXME there is prob a better way...
glMultMatrixf(mm)
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def _matrix(self):
"""return the rotation matrix for the trackball"""
return q_matrix(self.rot_quat)
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def _rotate(self, norm_mouse_x, norm_mouse_y):
"""Pass the x and y coordinates of the last and current positions of
the mouse, scaled so they are in the range [-1.0,1.0].
Simulate a track-ball. Project the points onto the virtual
trackball, then figure out the axis of rotation, which is the cross
product of LAST NEW and O LAST (O is the center of the ball, 0,0,0)
Note: This is a deformed trackball-- is a trackball in the center,
but is deformed into a hyperbolic sheet of rotation away from the
center. This particular function was chosen after trying out
several variations.
"""
# handle special case
if (self.last_x == norm_mouse_x and self.last_y == norm_mouse_y):
# Zero rotation
return [ 0.0, 0.0, 0.0, 1.0]
#
# First, figure out z-coordinates for projection of P1 and P2 to
# deformed sphere
#
last = [self.last_x, self.last_y, project_z(self.TRACKBALLSIZE,self.last_x,self.last_y)]
new = [norm_mouse_x, norm_mouse_y, project_z(self.TRACKBALLSIZE,norm_mouse_x,norm_mouse_y)]
#
# Now, we want the cross product of LAST and NEW
# aka the axis of rotation
#
a = v3cross(new,last)
#
# Figure out how much to rotate around that axis (phi)
#
d = v3sub(last,new)
t = v3length(d) / (2.0*self.TRACKBALLSIZE)
# Avoid problems with out-of-control values...
if (t > 1.0): t = 1.0
if (t < -1.0): t = -1.0
phi = 2.0 * math.asin(t)
return q_from_axis_angle(a,phi)