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..net/t3swing/article/details/78471135