一、目的
1、正弦波叠加为方波的GLSL实现；
二、程序运行结果
三、正弦波合成方波的处理
1、傅里叶函数分解方波公式：
f(y) = 4/PI * (sinx+ sin3x/3 + sin5x/5 + ...);
2、实际程序里面公式为：
f(y) = sinx+ sin3x/3 + sin5x/5 + ...
3、键盘控制
加入了正弦波合成方波的处理，使用箭头键移动正弦波，使用上下箭头进行振幅调整，使用+，-号来调整正弦波叠加的次数。
四、源代码
"""
glfw_sin02.py
Author: dalong10
Description: Draw a SquareWave, learning OPENGL
"""
import glutils #Common OpenGL utilities,see glutils.py
import sys, random, math
import OpenGL
from OpenGL.GL import *
from OpenGL.GL.shaders import *
import numpy
import numpy as np
import glfw
strVS = """
#version 330 core
layout (location = 0) in float vertexSerial;
uniform int g_sinCnt;
uniform float g_rangeL;
uniform float g_rangeR;
uniform float g_amplitud;
const int sampleCnt=200;
vec2 createSinPostion(float posIdex,float factor,float amplitude, float rangeL, float rangeR)
{ vec2 sinPos;
float range = rangeR - rangeL;
sinPos.x = (2.0 * posIdex - sampleCnt)/sampleCnt;
sinPos.y = amplitude * sin(factor * (rangeL + posIdex * range / sampleCnt));
return sinPos;
}
vec2 createSquareWave(float posIdex,int sinCnt, float amplitude, float rangeL, float rangeR)
{ vec2 SquareWarvePos, sinPos;
int i = 0;
for (i = 0;i<100 ; i++)
{ int f = 2 * i + 1;
sinPos =createSinPostion(posIdex, 1.0 * f, 1.0 / f, rangeL, rangeR);
SquareWarvePos.x = sinPos.x;
SquareWarvePos.y += (sinPos.y * amplitude);
if (i>=sinCnt) return SquareWarvePos;
}
return SquareWarvePos;
}
void main(){
vec2 SquareWarvePos = createSquareWave(vertexSerial,g_sinCnt,g_amplitud,g_rangeL,g_rangeR);
gl_Position = vec4(SquareWarvePos,0.0,1.0);
}
"""
strFS = """
#version 330 core
out vec3 color;
void main(){
color = vec3(1,1,0);
}
"""
class FirstSinCurve:
def __init__(self):
global sinCntIdx
global rangeLIdx
global rangeRIdx
global amplitudIdx
global g_sinCnt
global g_rangeL
global g_rangeR
global g_amplitud
sampleCnt=200
# load shaders
self.program = glutils.loadShaders(strVS, strFS)
glUseProgram(self.program)
# attributes
sinCntIdx = glGetUniformLocation(self.program, "g_sinCnt");
rangeLIdx = glGetUniformLocation(self.program, "g_rangeL");
rangeRIdx = glGetUniformLocation(self.program, "g_rangeR");
amplitudIdx = glGetUniformLocation(self.program, "g_amplitud");
# set up VBOs
vertexSerial = np.zeros(200, np.float32)
for i in range(sampleCnt):
vertexSerial[i] = i
self.vertexBuffer = glGenBuffers(1)
glBindBuffer(GL_ARRAY_BUFFER, self.vertexBuffer)
glBufferData(GL_ARRAY_BUFFER, 4*len(vertexSerial), vertexSerial, GL_STATIC_DRAW)
# Position attribute
glVertexAttribPointer(0, 1, GL_FLOAT, GL_FALSE, 0,None)
# enable arrays
glEnableVertexAttribArray(0)
def render(self):
global sinCntIdx
global rangeLIdx
global rangeRIdx
global amplitudIdx
global g_sinCnt
global g_rangeL
global g_rangeR
global g_amplitud
# use shader
sampleCnt=200
glUseProgram(self.program)
glUniform1i(sinCntIdx,g_sinCnt)
glUniform1f(rangeLIdx,g_rangeL)
glUniform1f(rangeRIdx,g_rangeR)
glUniform1f(amplitudIdx,g_amplitud)
# set up VBOs
vertexSerial = np.zeros(200, np.float32)
for i in range(sampleCnt):
vertexSerial[i] = i
self.vertexBuffer = glGenBuffers(1)
glBindBuffer(GL_ARRAY_BUFFER, self.vertexBuffer)
glBufferData(GL_ARRAY_BUFFER, 4*len(vertexSerial), vertexSerial, GL_STATIC_DRAW)
# Position attribute
glVertexAttribPointer(0, 1, GL_FLOAT, GL_FALSE, 0,None)
# enable arrays
glEnableVertexAttribArray(0)
# draw
glDrawArrays(GL_LINE_STRIP, 0, 200)
glFlush()
if __name__ == '__main__':
import sys
import glfw
import OpenGL.GL as gl
global g_sinCnt
global g_rangeL
global g_rangeR
global g_amplitud
PI = 3.14159265358979323846264
g_sinCnt = 5
g_rangeL = -3 * PI
g_rangeR = 3 * PI
g_amplitud = 1.0
def on_key(window, key, scancode, action, mods):
global g_sinCnt
global g_rangeL
global g_rangeR
global g_amplitud
if action == glfw.PRESS:
if key == glfw.KEY_ESCAPE :
glfw.set_window_should_close(window,1)
elif key == glfw.KEY_KP_ADD or key == glfw.KEY_A:
if (g_sinCnt < 100):
g_sinCnt+=1
elif key == glfw.KEY_KP_SUBTRACT or key == glfw.KEY_D:
if (g_sinCnt >=1):
g_sinCnt-=1
elif key == glfw.KEY_UP:
if (g_amplitud < 2):
g_amplitud += 0.1
elif key == glfw.KEY_DOWN:
if (g_amplitud > 0.3):
g_amplitud -= 0.1
elif key == glfw.KEY_LEFT:
g_rangeL -= 0.1
g_rangeR -= 0.1
elif key == glfw.KEY_RIGHT:
g_rangeL += 0.1
g_rangeR += 0.1
print('g_sinCnt=',g_sinCnt)
# Initialize the library
if not glfw.init():
sys.exit()
# Create a windowed mode window and its OpenGL context
window = glfw.create_window(300, 300, "draw SquareWave ", None, None)
if not window:
glfw.terminate()
sys.exit()
# Make the window's context current
glfw.make_context_current(window)
# Install a key handler
glfw.set_key_callback(window, on_key)
# Loop until the user closes the window
firstSinCurve0 = FirstSinCurve()
while not glfw.window_should_close(window):
# Render here
width, height = glfw.get_framebuffer_size(window)
ratio = width / float(height)
gl.glViewport(0, 0, width, height)
gl.glClear(gl.GL_COLOR_BUFFER_BIT)
gl.glClearColor(0.0,0.0,4.0,0.0)
firstSinCurve0.render()
# Swap front and back buffers
glfw.swap_buffers(window)
# Poll for and process events
glfw.poll_events()
glfw.terminate()
五、参考文献
1、他山随悟博客https://blog.csdn.net/t3swing/article/details/78471135