如何在 Pyopengl 中从 3-D numpy 数组创建表面？
How to create surface from 3-D numpy array in Pyopengl?
我创建了一个由 X、Y 和 Z 轴坐标组成的 3 维 numpy 数组。现在我正在尝试使用 opengl 中的这些点创建一个表面，但我所取得的成功是创建如下所示的线模型 。任何人都可以建议更改我的代码以根据数据形成实际的 3-D 表面吗？
使用的数据文件 link https://drive.google.com/open?id=1PWbNIt3xbchtQ9HIIS96k7ZjblzPO_wO
代码：-
import OpenGL.GL as gl
import OpenGL.arrays.vbo as glvbo
from PyQt5.Qt import *
import numpy as np
import Backend_algo as Sb
import sys
import ctypes
def compile_vertex_shader(source):
"""Compile a vertex shader from source."""
vertex_shader = gl.glCreateShader(gl.GL_VERTEX_SHADER)
gl.glShaderSource(vertex_shader, source)
gl.glCompileShader(vertex_shader)
# check compilation error
result = gl.glGetShaderiv(vertex_shader, gl.GL_COMPILE_STATUS)
if not (result):
raise RuntimeError(gl.glGetShaderInfoLog(vertex_shader))
return vertex_shader
def compile_fragment_shader(source):
"""Compile a fragment shader from source."""
fragment_shader = gl.glCreateShader(gl.GL_FRAGMENT_SHADER)
gl.glShaderSource(fragment_shader, source)
gl.glCompileShader(fragment_shader)
result = gl.glGetShaderiv(fragment_shader, gl.GL_COMPILE_STATUS)
if not (result):
raise RuntimeError(gl.glGetShaderInfoLog(fragment_shader))
return fragment_shader
def link_shader_program(vertex_shader, fragment_shader):
"""Create a shader program with from compiled shaders."""
program = gl.glCreateProgram()
gl.glAttachShader(program, vertex_shader)
gl.glAttachShader(program, fragment_shader)
gl.glLinkProgram(program)
result = gl.glGetProgramiv(program, gl.GL_LINK_STATUS)
if not (result):
raise RuntimeError(gl.glGetProgramInfoLog(program))
return program
VS = '''
attribute vec3 position;
uniform float right;
uniform float bottom;
uniform float left;
uniform float top;
uniform float far;
uniform float near;
void main() {
mat4 testmat = mat4(
vec4(2.0 / (right - left), 0, 0, 0),
vec4(0, 2.0 / (top - bottom), 0, 0),
vec4(0, 0, -2.0 / (far - near), 0),
vec4(-(right + left) / (right - left), -(top + bottom) / (top - bottom), -(far + near) / (far - near), 1)
);
gl_Position = testmat * vec4(position, 1.);
}
'''
FS = '''
#version 450
// Output variable of the fragment shader, which is a 4D vector containing the
// RGBA components of the pixel color.
uniform vec3 triangleColor;
out vec4 outColor;
void main()
{
outColor = vec4(triangleColor, 1.0);
}
'''
class GLPlotWidget3D(QGLWidget):
def __init__(self, *args):
# QGLWidget.__init__(self)
super(GLPlotWidget3D, self).__init__()
# self.parent = args[0]
self.width, self.height = 100, 100
self.right, self.left, self.top, self.bottom = 21000, -21000, 10, -10
self.data = np.zeros((3, 10, 2))
self.vbo = glvbo.VBO(self.data)
self.showMaximized()
def initializeGL(self):
vs = Sb.compile_vertex_shader(VS)
fs = Sb.compile_fragment_shader(FS)
self.shaders_program = link_shader_program(vs, fs)
self.e = np.load(('three.npy'), mmap_mode='r')
self.e = np.array(self.e, dtype=np.float32)
self.right, self.left, self.top, self.bottom, self.far, self.near = self.e[:, :, 1].min(), self.e[:, : , 1].max(), self.e[:, : , 0].min(), self.e[:, : , 0].max(), self.e[:, : , 2].max(), self.e[:, : , 2].min()
def ortho_view(self):
right = gl.glGetUniformLocation(self.shaders_program, "right")
gl.glUniform1f(right, self.right)
left = gl.glGetUniformLocation(self.shaders_program, "left")
gl.glUniform1f(left, self.left)
top = gl.glGetUniformLocation(self.shaders_program, "top")
gl.glUniform1f(top, self.top)
bottom = gl.glGetUniformLocation(self.shaders_program, "bottom")
gl.glUniform1f(bottom, self.bottom)
far = gl.glGetUniformLocation(self.shaders_program, "far")
gl.glUniform1f(far, self.far)
near = gl.glGetUniformLocation(self.shaders_program, "near")
gl.glUniform1f(near, self.near)
def paintGL(self):
self.resizeGL(self.width, self.height)
gl.glClearColor(0.2, 0.2, 0.2, 0)
gl.glClear(gl.GL_COLOR_BUFFER_BIT)
gl.glUseProgram(self.shaders_program)
buffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, buffer)
stride = self.e.strides[0]
offset = ctypes.c_void_p(1)
loc = gl.glGetAttribLocation(self.shaders_program, "position")
gl.glEnableVertexAttribArray(loc)
gl.glVertexAttribPointer(loc, 3, gl.GL_FLOAT, False, stride, offset)
gl.glBufferData(gl.GL_ARRAY_BUFFER, self.e.nbytes, self.e, gl.GL_DYNAMIC_DRAW)
gl.glDrawArrays(gl.GL_LINE_LOOP, 0, self.e.shape[0])
self.ortho_view()
uni_color = gl.glGetUniformLocation(self.shaders_program, "triangleColor")
gl.glUniform3f(uni_color, 0.9, 0.9, 0.9)
def resizeGL(self, width, height):
self.width, self.height = width, height
gl.glViewport(0, 0, width, height)
def main():
app = QApplication(sys.argv)
editor = GLPlotWidget3D()
editor.show()
sys.exit(app.exec_())
if __name__ == '__main__':
main()
'three.npy' 包含一个带有管顶点坐标的 3 维数组 (7782 x 24 x3)。大小为 3 的第 3 个维度包含顶点的 x、y 和 z 坐标。顶点被组织成 7782 个环，圆周上有 24 个点。
将顶点坐标读取到展平缓冲区（numpy 数组由 glBufferData 自动展平）。
生成一个索引数组（顶点缓冲区的索引）。这些索引描述了 GL_TRIANGLE_STRIP 个原语，这些原语堆叠了 7781 个环。每个圆环由 24 个圆周组成。
self.e = np.load(('three.npy'), mmap_mode='r')
self.e = np.array(self.e, dtype=np.float32)
self.elems = []
ring_c = self.e.shape[1]
slice_c = self.e.shape[0]
for si in range(slice_c-1):
self.elems += [si*ring_c, si*ring_c]
for ri in range(ring_c+1):
ie = ri % ring_c
self.elems += [ie+si*ring_c, ie+(si+1)*ring_c]
self.elems = np.array(self.elems, dtype=np.int32)
顶点的x和y分量在[-10, 10]范围内，但z分量在范围内[3、29724672]。
x min x max y min y max z min z max
-10.589109 10.517833 -10.464569 10.594374 29724672.0 3.1618009
我建议为 z 坐标定义一个比例：
self.scaleZ = 0.000001
为索引创建一个 Vertex Buffer Object (GL_ARRAY_BUFFER) for the vertices and an Index buffer Object (GL_ELEMENT_ARRAY_BUFFER):
self.vertexbuffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertexbuffer)
gl.glBufferData(gl.GL_ARRAY_BUFFER, self.e, gl.GL_DYNAMIC_DRAW)
self.elementbuffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, self.elementbuffer)
gl.glBufferData(gl.GL_ELEMENT_ARRAY_BUFFER, self.elems, gl.GL_DYNAMIC_DRAW)
指定顶点坐标数组。参见 Vertex Specification。
stride和offset parameter of glVertexAttribPointer have to be 0.
stride 指定连续通用顶点属性之间的字节偏移量，它必须是 3*self.e.itemsize (12) 或 0。 0 具有特殊含义，并且将属性解释为紧密打包。如果 stride 为 0，则由 size 和 type 参数计算。
offset必须是ctypes.c_void_p(0)或None，因为1属性在数组中的偏移量是0.
在任何情况下，stride 和 offset 的单位都是字节。
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertexbuffer)
stride = 0 # 3*self.e.itemsize
offset = None # ctypes.c_void_p(0)
loc = self.attrib['position']
gl.glEnableVertexAttribArray(loc)
gl.glVertexAttribPointer(loc, 3, gl.GL_FLOAT, False, stride, offset)
primitive type is GL_TRIANGLE_STRIP and the index buffer has to be bound before the elements are drawn by glDrawElements:
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, self.elementbuffer)
self.perspective_view()
gl.glUniform3f(self.uniform['triangleColor'], 1, 1, 1)
gl.glDrawElements(gl.GL_TRIANGLE_STRIP, self.elems.size, gl.GL_UNSIGNED_INT, None)
而不是为投影指定 Orthographic projection matrix in the vertex shader, I recommend to use matrix Uniform variable，分别为模型和视图转换。
投影矩阵定义了 3 维观察体积到 2 维视口的投影。视图矩阵定义了视图的观察位置和场景的观察方向。模型矩阵定义了模式的比例和动画。
attribute vec3 position;
uniform mat4 u_proj;
uniform mat4 u_view;
uniform mat4 u_model;
void main() {
gl_Position = u_proj * u_view * u_model * vec4(position, 1.0);
}
获取着色器程序链接后的属性索引和统一位置：
vs = compile_vertex_shader(VS)
fs = compile_fragment_shader(FS)
self.shaders_program = link_shader_program(vs, fs)
self.attrib = { a : gl.glGetAttribLocation (self.shaders_program, a) for a in ['position'] }
print(self.attrib)
self.uniform = { u : gl.glGetUniformLocation (self.shaders_program, u) for u in ['u_model', 'u_view', 'u_proj', "triangleColor"] }
print(self.uniform)
对于 3D 外观，我建议使用 Perspective projection rather than Orthographic projection。
使用numpy.array or numpy.matrix设置矩阵。
# projection matrix
aspect, ta, near, far = self.width/self.height, np.tan(np.radians(90.0) / 2), 0.1, 50
proj = np.matrix(((1/ta/aspect, 0, 0, 0), (0, 1/ta, 0, 0), (0, 0, -(far+near)/(far-near), -1), (0, 0, -2*far*near/(far-near), 0)), np.float32)
# view matrix
view = np.matrix(((1, 0, 0, 0), (0, 0, -1, 0), (0, 1, 0, 0), (0, 0, -30, 1)), np.float32)
# model matrix
c, s = math.cos(self.angle), math.sin(self.angle)
model = scale
gl.glUniformMatrix4fv(self.uniform['u_proj'], 1, gl.GL_FALSE, proj)
gl.glUniformMatrix4fv(self.uniform['u_view'], 1, gl.GL_FALSE, view)
gl.glUniformMatrix4fv(self.uniform['u_model'], 1, gl.GL_FALSE, model)
完整示例：
（片段着色器根据片段的深度对片段进行着色）
import OpenGL.GL as gl
import OpenGL.arrays.vbo as glvbo
from PyQt5.Qt import *
import numpy as np
#import Backend_algo as Sb
import sys
import ctypes
import os
import math
sourceFileDir = os.path.dirname(os.path.abspath(__file__))
def compile_vertex_shader(source):
"""Compile a vertex shader from source."""
vertex_shader = gl.glCreateShader(gl.GL_VERTEX_SHADER)
gl.glShaderSource(vertex_shader, source)
gl.glCompileShader(vertex_shader)
# check compilation error
result = gl.glGetShaderiv(vertex_shader, gl.GL_COMPILE_STATUS)
if not (result):
raise RuntimeError(gl.glGetShaderInfoLog(vertex_shader))
return vertex_shader
def compile_fragment_shader(source):
"""Compile a fragment shader from source."""
fragment_shader = gl.glCreateShader(gl.GL_FRAGMENT_SHADER)
gl.glShaderSource(fragment_shader, source)
gl.glCompileShader(fragment_shader)
result = gl.glGetShaderiv(fragment_shader, gl.GL_COMPILE_STATUS)
if not (result):
raise RuntimeError(gl.glGetShaderInfoLog(fragment_shader))
return fragment_shader
def link_shader_program(vertex_shader, fragment_shader):
"""Create a shader program with from compiled shaders."""
program = gl.glCreateProgram()
gl.glAttachShader(program, vertex_shader)
gl.glAttachShader(program, fragment_shader)
gl.glLinkProgram(program)
result = gl.glGetProgramiv(program, gl.GL_LINK_STATUS)
if not (result):
raise RuntimeError(gl.glGetProgramInfoLog(program))
return program
VS = '''
attribute vec3 position;
uniform mat4 u_proj;
uniform mat4 u_view;
uniform mat4 u_model;
void main() {
gl_Position = u_proj * u_view * u_model * vec4(position, 1.0);
}
'''
FS = '''
#version 450
out vec4 outColor;
uniform vec3 triangleColor;
void main()
{
float d = 1.0 - gl_FragCoord.z;
outColor = vec4(triangleColor * d, 1.0);
}
'''
class GLPlotWidget3D(QGLWidget):
def __init__(self, *args):
# QGLWidget.__init__(self)
super(GLPlotWidget3D, self).__init__()
# self.parent = args[0]
self.width, self.height = 100, 100
self.right, self.left, self.top, self.bottom = 21000, -21000, 10, -10
self.data = np.zeros((3, 10, 2))
self.vbo = glvbo.VBO(self.data)
self.showMaximized()
def initializeGL(self):
vs = compile_vertex_shader(VS)
fs = compile_fragment_shader(FS)
self.shaders_program = link_shader_program(vs, fs)
self.attrib = { a : gl.glGetAttribLocation (self.shaders_program, a) for a in ['position'] }
print(self.attrib)
self.uniform = { u : gl.glGetUniformLocation (self.shaders_program, u) for u in ['u_model', 'u_view', 'u_proj', "triangleColor"] }
print(self.uniform)
self.e = np.load((os.path.join(sourceFileDir,'three.npy')), mmap_mode='r')
self.e = np.array(self.e, dtype=np.float32)
print(self.e.shape)
self.elems = []
ring_c = self.e.shape[1]
slice_c = self.e.shape[0]
for si in range(slice_c-1):
self.elems += [si*ring_c, si*ring_c]
for ri in range(ring_c+1):
ie = ri % ring_c
self.elems += [ie+si*ring_c, ie+(si+1)*ring_c]
self.elems = np.array(self.elems, dtype=np.int32)
self.vertexbuffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertexbuffer)
gl.glBufferData(gl.GL_ARRAY_BUFFER, self.e, gl.GL_DYNAMIC_DRAW)
self.elementbuffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, self.elementbuffer)
gl.glBufferData(gl.GL_ELEMENT_ARRAY_BUFFER, self.elems, gl.GL_DYNAMIC_DRAW)
self.scaleZ = 0.000001
self.right, self.left, self.top, self.bottom, self.far, self.near = self.e[:, :, 1].min(), self.e[:, : , 1].max(), self.e[:, : , 0].min(), self.e[:, : , 0].max(), self.e[:, : , 2].max(), self.e[:, : , 2].min()
print(self.right, self.left, self.top, self.bottom, self.far, self.near)
self.far *= self.scaleZ
self.near *= self.scaleZ
self.angle = 0.0
self.GLtimer = QTimer()
self.GLtimer.setInterval(10)
self.GLtimer.timeout.connect(self.redraw)
self.GLtimer.start()
def redraw(self):
self.angle += 0.01
self.update()
def perspective_view(self):
# projection matrix
aspect, ta, near, far = self.width/self.height, np.tan(np.radians(90.0) / 2), 10, 50
proj = np.matrix(((1/ta/aspect, 0, 0, 0), (0, 1/ta, 0, 0), (0, 0, -(far+near)/(far-near), -1), (0, 0, -2*far*near/(far-near), 0)), np.float32)
# view matrix
view = np.matrix(((1, 0, 0, 0), (0, 0, -1, 0), (0, 1, 0, 0), (0, 0, -30, 1)), np.float32)
# model matrix
c, s = math.cos(self.angle), math.sin(self.angle)
scale = np.matrix(((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, self.scaleZ, 0), (0, 0, 0, 1)), np.float32)
rotZ = np.array(((c, s, 0, 0), (-s, c, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)), np.float32)
rotY = np.matrix(((0, 0, 1, 0), (0, 1, 0, 0), (-1, 0, 0, 0), (0, 0, 0, 1)), np.float32)
trans = np.matrix(((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, (self.near - self.far)/2, 1)), np.float32)
model = scale * trans * rotY * rotZ
gl.glUniformMatrix4fv(self.uniform['u_proj'], 1, gl.GL_FALSE, proj)
gl.glUniformMatrix4fv(self.uniform['u_view'], 1, gl.GL_FALSE, view)
gl.glUniformMatrix4fv(self.uniform['u_model'], 1, gl.GL_FALSE, model)
def paintGL(self):
self.resizeGL(self.width, self.height)
gl.glClearColor(0.2, 0.2, 0.2, 0)
gl.glClear(gl.GL_COLOR_BUFFER_BIT | gl.GL_DEPTH_BUFFER_BIT)
gl.glEnable(gl.GL_DEPTH_TEST)
gl.glUseProgram(self.shaders_program)
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertexbuffer)
stride = 0 # 3*self.e.itemsize
offset = None # ctypes.c_void_p(0)
loc = self.attrib['position']
gl.glEnableVertexAttribArray(loc)
gl.glVertexAttribPointer(loc, 3, gl.GL_FLOAT, False, stride, offset)
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, self.elementbuffer)
self.perspective_view()
gl.glUniform3f(self.uniform['triangleColor'], 1, 1, 1)
#gl.glPolygonMode(gl.GL_FRONT_AND_BACK, gl.GL_LINE)
gl.glDrawElements(gl.GL_TRIANGLE_STRIP, self.elems.size, gl.GL_UNSIGNED_INT, None)
def resizeGL(self, width, height):
self.width, self.height = width, height
gl.glViewport(0, 0, width, height)
def main():
app = QApplication(sys.argv)
editor = GLPlotWidget3D()
editor.show()
sys.exit(app.exec_())
if __name__ == '__main__':
main()
我创建了一个由 X、Y 和 Z 轴坐标组成的 3 维 numpy 数组。现在我正在尝试使用 opengl 中的这些点创建一个表面，但我所取得的成功是创建如下所示的线模型
代码：-
import OpenGL.GL as gl
import OpenGL.arrays.vbo as glvbo
from PyQt5.Qt import *
import numpy as np
import Backend_algo as Sb
import sys
import ctypes
def compile_vertex_shader(source):
"""Compile a vertex shader from source."""
vertex_shader = gl.glCreateShader(gl.GL_VERTEX_SHADER)
gl.glShaderSource(vertex_shader, source)
gl.glCompileShader(vertex_shader)
# check compilation error
result = gl.glGetShaderiv(vertex_shader, gl.GL_COMPILE_STATUS)
if not (result):
raise RuntimeError(gl.glGetShaderInfoLog(vertex_shader))
return vertex_shader
def compile_fragment_shader(source):
"""Compile a fragment shader from source."""
fragment_shader = gl.glCreateShader(gl.GL_FRAGMENT_SHADER)
gl.glShaderSource(fragment_shader, source)
gl.glCompileShader(fragment_shader)
result = gl.glGetShaderiv(fragment_shader, gl.GL_COMPILE_STATUS)
if not (result):
raise RuntimeError(gl.glGetShaderInfoLog(fragment_shader))
return fragment_shader
def link_shader_program(vertex_shader, fragment_shader):
"""Create a shader program with from compiled shaders."""
program = gl.glCreateProgram()
gl.glAttachShader(program, vertex_shader)
gl.glAttachShader(program, fragment_shader)
gl.glLinkProgram(program)
result = gl.glGetProgramiv(program, gl.GL_LINK_STATUS)
if not (result):
raise RuntimeError(gl.glGetProgramInfoLog(program))
return program
VS = '''
attribute vec3 position;
uniform float right;
uniform float bottom;
uniform float left;
uniform float top;
uniform float far;
uniform float near;
void main() {
mat4 testmat = mat4(
vec4(2.0 / (right - left), 0, 0, 0),
vec4(0, 2.0 / (top - bottom), 0, 0),
vec4(0, 0, -2.0 / (far - near), 0),
vec4(-(right + left) / (right - left), -(top + bottom) / (top - bottom), -(far + near) / (far - near), 1)
);
gl_Position = testmat * vec4(position, 1.);
}
'''
FS = '''
#version 450
// Output variable of the fragment shader, which is a 4D vector containing the
// RGBA components of the pixel color.
uniform vec3 triangleColor;
out vec4 outColor;
void main()
{
outColor = vec4(triangleColor, 1.0);
}
'''
class GLPlotWidget3D(QGLWidget):
def __init__(self, *args):
# QGLWidget.__init__(self)
super(GLPlotWidget3D, self).__init__()
# self.parent = args[0]
self.width, self.height = 100, 100
self.right, self.left, self.top, self.bottom = 21000, -21000, 10, -10
self.data = np.zeros((3, 10, 2))
self.vbo = glvbo.VBO(self.data)
self.showMaximized()
def initializeGL(self):
vs = Sb.compile_vertex_shader(VS)
fs = Sb.compile_fragment_shader(FS)
self.shaders_program = link_shader_program(vs, fs)
self.e = np.load(('three.npy'), mmap_mode='r')
self.e = np.array(self.e, dtype=np.float32)
self.right, self.left, self.top, self.bottom, self.far, self.near = self.e[:, :, 1].min(), self.e[:, : , 1].max(), self.e[:, : , 0].min(), self.e[:, : , 0].max(), self.e[:, : , 2].max(), self.e[:, : , 2].min()
def ortho_view(self):
right = gl.glGetUniformLocation(self.shaders_program, "right")
gl.glUniform1f(right, self.right)
left = gl.glGetUniformLocation(self.shaders_program, "left")
gl.glUniform1f(left, self.left)
top = gl.glGetUniformLocation(self.shaders_program, "top")
gl.glUniform1f(top, self.top)
bottom = gl.glGetUniformLocation(self.shaders_program, "bottom")
gl.glUniform1f(bottom, self.bottom)
far = gl.glGetUniformLocation(self.shaders_program, "far")
gl.glUniform1f(far, self.far)
near = gl.glGetUniformLocation(self.shaders_program, "near")
gl.glUniform1f(near, self.near)
def paintGL(self):
self.resizeGL(self.width, self.height)
gl.glClearColor(0.2, 0.2, 0.2, 0)
gl.glClear(gl.GL_COLOR_BUFFER_BIT)
gl.glUseProgram(self.shaders_program)
buffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, buffer)
stride = self.e.strides[0]
offset = ctypes.c_void_p(1)
loc = gl.glGetAttribLocation(self.shaders_program, "position")
gl.glEnableVertexAttribArray(loc)
gl.glVertexAttribPointer(loc, 3, gl.GL_FLOAT, False, stride, offset)
gl.glBufferData(gl.GL_ARRAY_BUFFER, self.e.nbytes, self.e, gl.GL_DYNAMIC_DRAW)
gl.glDrawArrays(gl.GL_LINE_LOOP, 0, self.e.shape[0])
self.ortho_view()
uni_color = gl.glGetUniformLocation(self.shaders_program, "triangleColor")
gl.glUniform3f(uni_color, 0.9, 0.9, 0.9)
def resizeGL(self, width, height):
self.width, self.height = width, height
gl.glViewport(0, 0, width, height)
def main():
app = QApplication(sys.argv)
editor = GLPlotWidget3D()
editor.show()
sys.exit(app.exec_())
if __name__ == '__main__':
main()
'three.npy' 包含一个带有管顶点坐标的 3 维数组 (7782 x 24 x3)。大小为 3 的第 3 个维度包含顶点的 x、y 和 z 坐标。顶点被组织成 7782 个环，圆周上有 24 个点。
将顶点坐标读取到展平缓冲区（numpy 数组由 glBufferData 自动展平）。
生成一个索引数组（顶点缓冲区的索引）。这些索引描述了 GL_TRIANGLE_STRIP 个原语，这些原语堆叠了 7781 个环。每个圆环由 24 个圆周组成。
self.e = np.load(('three.npy'), mmap_mode='r')
self.e = np.array(self.e, dtype=np.float32)
self.elems = []
ring_c = self.e.shape[1]
slice_c = self.e.shape[0]
for si in range(slice_c-1):
self.elems += [si*ring_c, si*ring_c]
for ri in range(ring_c+1):
ie = ri % ring_c
self.elems += [ie+si*ring_c, ie+(si+1)*ring_c]
self.elems = np.array(self.elems, dtype=np.int32)
顶点的x和y分量在[-10, 10]范围内，但z分量在范围内[3、29724672]。
x min x max y min y max z min z max
-10.589109 10.517833 -10.464569 10.594374 29724672.0 3.1618009
我建议为 z 坐标定义一个比例：
self.scaleZ = 0.000001
为索引创建一个 Vertex Buffer Object (GL_ARRAY_BUFFER) for the vertices and an Index buffer Object (GL_ELEMENT_ARRAY_BUFFER):
self.vertexbuffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertexbuffer)
gl.glBufferData(gl.GL_ARRAY_BUFFER, self.e, gl.GL_DYNAMIC_DRAW)
self.elementbuffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, self.elementbuffer)
gl.glBufferData(gl.GL_ELEMENT_ARRAY_BUFFER, self.elems, gl.GL_DYNAMIC_DRAW)
指定顶点坐标数组。参见 Vertex Specification。
stride和offset parameter of glVertexAttribPointer have to be 0.
stride 指定连续通用顶点属性之间的字节偏移量，它必须是 3*self.e.itemsize (12) 或 0。 0 具有特殊含义，并且将属性解释为紧密打包。如果 stride 为 0，则由 size 和 type 参数计算。
offset必须是ctypes.c_void_p(0)或None，因为1属性在数组中的偏移量是0.
在任何情况下，stride 和 offset 的单位都是字节。
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertexbuffer)
stride = 0 # 3*self.e.itemsize
offset = None # ctypes.c_void_p(0)
loc = self.attrib['position']
gl.glEnableVertexAttribArray(loc)
gl.glVertexAttribPointer(loc, 3, gl.GL_FLOAT, False, stride, offset)
primitive type is GL_TRIANGLE_STRIP and the index buffer has to be bound before the elements are drawn by glDrawElements:
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, self.elementbuffer)
self.perspective_view()
gl.glUniform3f(self.uniform['triangleColor'], 1, 1, 1)
gl.glDrawElements(gl.GL_TRIANGLE_STRIP, self.elems.size, gl.GL_UNSIGNED_INT, None)
而不是为投影指定 Orthographic projection matrix in the vertex shader, I recommend to use matrix Uniform variable，分别为模型和视图转换。
投影矩阵定义了 3 维观察体积到 2 维视口的投影。视图矩阵定义了视图的观察位置和场景的观察方向。模型矩阵定义了模式的比例和动画。
attribute vec3 position;
uniform mat4 u_proj;
uniform mat4 u_view;
uniform mat4 u_model;
void main() {
gl_Position = u_proj * u_view * u_model * vec4(position, 1.0);
}
获取着色器程序链接后的属性索引和统一位置：
vs = compile_vertex_shader(VS)
fs = compile_fragment_shader(FS)
self.shaders_program = link_shader_program(vs, fs)
self.attrib = { a : gl.glGetAttribLocation (self.shaders_program, a) for a in ['position'] }
print(self.attrib)
self.uniform = { u : gl.glGetUniformLocation (self.shaders_program, u) for u in ['u_model', 'u_view', 'u_proj', "triangleColor"] }
print(self.uniform)
对于 3D 外观，我建议使用 Perspective projection rather than Orthographic projection。
使用numpy.array or numpy.matrix设置矩阵。
# projection matrix
aspect, ta, near, far = self.width/self.height, np.tan(np.radians(90.0) / 2), 0.1, 50
proj = np.matrix(((1/ta/aspect, 0, 0, 0), (0, 1/ta, 0, 0), (0, 0, -(far+near)/(far-near), -1), (0, 0, -2*far*near/(far-near), 0)), np.float32)
# view matrix
view = np.matrix(((1, 0, 0, 0), (0, 0, -1, 0), (0, 1, 0, 0), (0, 0, -30, 1)), np.float32)
# model matrix
c, s = math.cos(self.angle), math.sin(self.angle)
model = scale
gl.glUniformMatrix4fv(self.uniform['u_proj'], 1, gl.GL_FALSE, proj)
gl.glUniformMatrix4fv(self.uniform['u_view'], 1, gl.GL_FALSE, view)
gl.glUniformMatrix4fv(self.uniform['u_model'], 1, gl.GL_FALSE, model)
完整示例：
（片段着色器根据片段的深度对片段进行着色）
import OpenGL.GL as gl
import OpenGL.arrays.vbo as glvbo
from PyQt5.Qt import *
import numpy as np
#import Backend_algo as Sb
import sys
import ctypes
import os
import math
sourceFileDir = os.path.dirname(os.path.abspath(__file__))
def compile_vertex_shader(source):
"""Compile a vertex shader from source."""
vertex_shader = gl.glCreateShader(gl.GL_VERTEX_SHADER)
gl.glShaderSource(vertex_shader, source)
gl.glCompileShader(vertex_shader)
# check compilation error
result = gl.glGetShaderiv(vertex_shader, gl.GL_COMPILE_STATUS)
if not (result):
raise RuntimeError(gl.glGetShaderInfoLog(vertex_shader))
return vertex_shader
def compile_fragment_shader(source):
"""Compile a fragment shader from source."""
fragment_shader = gl.glCreateShader(gl.GL_FRAGMENT_SHADER)
gl.glShaderSource(fragment_shader, source)
gl.glCompileShader(fragment_shader)
result = gl.glGetShaderiv(fragment_shader, gl.GL_COMPILE_STATUS)
if not (result):
raise RuntimeError(gl.glGetShaderInfoLog(fragment_shader))
return fragment_shader
def link_shader_program(vertex_shader, fragment_shader):
"""Create a shader program with from compiled shaders."""
program = gl.glCreateProgram()
gl.glAttachShader(program, vertex_shader)
gl.glAttachShader(program, fragment_shader)
gl.glLinkProgram(program)
result = gl.glGetProgramiv(program, gl.GL_LINK_STATUS)
if not (result):
raise RuntimeError(gl.glGetProgramInfoLog(program))
return program
VS = '''
attribute vec3 position;
uniform mat4 u_proj;
uniform mat4 u_view;
uniform mat4 u_model;
void main() {
gl_Position = u_proj * u_view * u_model * vec4(position, 1.0);
}
'''
FS = '''
#version 450
out vec4 outColor;
uniform vec3 triangleColor;
void main()
{
float d = 1.0 - gl_FragCoord.z;
outColor = vec4(triangleColor * d, 1.0);
}
'''
class GLPlotWidget3D(QGLWidget):
def __init__(self, *args):
# QGLWidget.__init__(self)
super(GLPlotWidget3D, self).__init__()
# self.parent = args[0]
self.width, self.height = 100, 100
self.right, self.left, self.top, self.bottom = 21000, -21000, 10, -10
self.data = np.zeros((3, 10, 2))
self.vbo = glvbo.VBO(self.data)
self.showMaximized()
def initializeGL(self):
vs = compile_vertex_shader(VS)
fs = compile_fragment_shader(FS)
self.shaders_program = link_shader_program(vs, fs)
self.attrib = { a : gl.glGetAttribLocation (self.shaders_program, a) for a in ['position'] }
print(self.attrib)
self.uniform = { u : gl.glGetUniformLocation (self.shaders_program, u) for u in ['u_model', 'u_view', 'u_proj', "triangleColor"] }
print(self.uniform)
self.e = np.load((os.path.join(sourceFileDir,'three.npy')), mmap_mode='r')
self.e = np.array(self.e, dtype=np.float32)
print(self.e.shape)
self.elems = []
ring_c = self.e.shape[1]
slice_c = self.e.shape[0]
for si in range(slice_c-1):
self.elems += [si*ring_c, si*ring_c]
for ri in range(ring_c+1):
ie = ri % ring_c
self.elems += [ie+si*ring_c, ie+(si+1)*ring_c]
self.elems = np.array(self.elems, dtype=np.int32)
self.vertexbuffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertexbuffer)
gl.glBufferData(gl.GL_ARRAY_BUFFER, self.e, gl.GL_DYNAMIC_DRAW)
self.elementbuffer = gl.glGenBuffers(1)
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, self.elementbuffer)
gl.glBufferData(gl.GL_ELEMENT_ARRAY_BUFFER, self.elems, gl.GL_DYNAMIC_DRAW)
self.scaleZ = 0.000001
self.right, self.left, self.top, self.bottom, self.far, self.near = self.e[:, :, 1].min(), self.e[:, : , 1].max(), self.e[:, : , 0].min(), self.e[:, : , 0].max(), self.e[:, : , 2].max(), self.e[:, : , 2].min()
print(self.right, self.left, self.top, self.bottom, self.far, self.near)
self.far *= self.scaleZ
self.near *= self.scaleZ
self.angle = 0.0
self.GLtimer = QTimer()
self.GLtimer.setInterval(10)
self.GLtimer.timeout.connect(self.redraw)
self.GLtimer.start()
def redraw(self):
self.angle += 0.01
self.update()
def perspective_view(self):
# projection matrix
aspect, ta, near, far = self.width/self.height, np.tan(np.radians(90.0) / 2), 10, 50
proj = np.matrix(((1/ta/aspect, 0, 0, 0), (0, 1/ta, 0, 0), (0, 0, -(far+near)/(far-near), -1), (0, 0, -2*far*near/(far-near), 0)), np.float32)
# view matrix
view = np.matrix(((1, 0, 0, 0), (0, 0, -1, 0), (0, 1, 0, 0), (0, 0, -30, 1)), np.float32)
# model matrix
c, s = math.cos(self.angle), math.sin(self.angle)
scale = np.matrix(((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, self.scaleZ, 0), (0, 0, 0, 1)), np.float32)
rotZ = np.array(((c, s, 0, 0), (-s, c, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)), np.float32)
rotY = np.matrix(((0, 0, 1, 0), (0, 1, 0, 0), (-1, 0, 0, 0), (0, 0, 0, 1)), np.float32)
trans = np.matrix(((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, (self.near - self.far)/2, 1)), np.float32)
model = scale * trans * rotY * rotZ
gl.glUniformMatrix4fv(self.uniform['u_proj'], 1, gl.GL_FALSE, proj)
gl.glUniformMatrix4fv(self.uniform['u_view'], 1, gl.GL_FALSE, view)
gl.glUniformMatrix4fv(self.uniform['u_model'], 1, gl.GL_FALSE, model)
def paintGL(self):
self.resizeGL(self.width, self.height)
gl.glClearColor(0.2, 0.2, 0.2, 0)
gl.glClear(gl.GL_COLOR_BUFFER_BIT | gl.GL_DEPTH_BUFFER_BIT)
gl.glEnable(gl.GL_DEPTH_TEST)
gl.glUseProgram(self.shaders_program)
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertexbuffer)
stride = 0 # 3*self.e.itemsize
offset = None # ctypes.c_void_p(0)
loc = self.attrib['position']
gl.glEnableVertexAttribArray(loc)
gl.glVertexAttribPointer(loc, 3, gl.GL_FLOAT, False, stride, offset)
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, self.elementbuffer)
self.perspective_view()
gl.glUniform3f(self.uniform['triangleColor'], 1, 1, 1)
#gl.glPolygonMode(gl.GL_FRONT_AND_BACK, gl.GL_LINE)
gl.glDrawElements(gl.GL_TRIANGLE_STRIP, self.elems.size, gl.GL_UNSIGNED_INT, None)
def resizeGL(self, width, height):
self.width, self.height = width, height
gl.glViewport(0, 0, width, height)
def main():
app = QApplication(sys.argv)
editor = GLPlotWidget3D()
editor.show()
sys.exit(app.exec_())
if __name__ == '__main__':
main()