OpenGL 中的旋轉立方體

Question

我想要一個圍繞中心旋轉的立方體。 這是我可以用這個轉換做的事情：

model = glm::rotate(identity, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0)); //rotate around y-axis
model = glm::translate(model, glm::vec3(8.0, 0.0, 0.0));
model = glm::rotate(model, glm::radians(-100.0f * time), glm::vec3(1.0, 0.0, 0.0)); //self-rotation

現在我想要一個立方體，當它圍繞 y 軸旋轉時，它會圍繞第一個立方體旋轉。 想象第一個立方體是地球，第二個立方體是月球。 我試過這個，但它沒有用。

test = glm::rotate(test, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0));
test = glm::translate(test, glm::vec3(3.0, 0.0, 0.0));
test = glm::translate(test, glm::vec3(8.0, 0.0, 0.0));
test = glm::rotate(test, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0));
test = glm::translate(test, glm::vec3(-8.0, 0.0, 0.0));
test = glm::rotate(test, glm::radians(-100.0f * time), glm::vec3(1.0, 0.0, 0.0)); // self-rotation

任何想法我做錯了什么？ 這是旋轉的圖片：

Answer 1

您的評論建議您有以下操作順序：

mvp = m_projection*m_view*m_model
vertex' = mvp*vertex

意思是m_view是視圖的逆矩陣，而m_model是實際網格的直接矩陣。

因此，您應該設置一次m_projection和m_view ，然后只更新m_model 。

我不使用 GLM（有我自己的數學庫）但是 IIRC 他們模仿舊的固定管道矩陣數學。 所以當我這樣做時（C++/VCL/OpenGL/GLSL ......我知道這些點應該是 VBO/VAO 我只是想快速測試）：

//---------------------------------------------------------------------------
//    ang   ,ang speed,body r,orbit r
//    [deg] ,[deg/s]   [unit],[unit]
float                  rs=1.0;          // star
float a0=0.0,da0= 50.0,r0=0.5,R0= 7.0;  // planet
float a1=0.0,da1=200.0,r1=0.2,R1= 1.0;  // moon
float a2=0.0,da2=250.0,r2=0.2,R2= 1.5;  // moon
float a3=0.0,da3= 20.0,r3=0.5,R3=10.0;  // planet
float a4=0.0,da4=150.0,r4=0.2,R4= 1.0;  // moon
float a5=0.0,da5=180.0,r5=0.2,R5= 1.5;  // moon
float b =0.0,db =50.0;                  // common self rotation
//---------------------------------------------------------------------------
void gl_draw()
    {
    GLint ix;
    GLfloat mp[16],mv[16],mm[16],m0[16];
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    float aspect=float(xs)/float(ys);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluPerspective(60.0/aspect,aspect,0.1,100.0);
    glGetFloatv(GL_PROJECTION_MATRIX,mp);
    glMatrixMode(GL_TEXTURE);
    glLoadIdentity();
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glTranslatef(0.0,0.0,-25.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mv);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glGetFloatv(GL_MODELVIEW_MATRIX,mm);

    glDisable(GL_DEPTH_TEST);
    glDisable(GL_TEXTURE_2D);
    glDisable(GL_CULL_FACE);
//  glEnable(GL_CULL_FACE);

    // GLSL sphere shader
    glUseProgram(prog_id);
    ix=glGetUniformLocation(prog_id,"m_projection"); glUniformMatrix4fv(ix,1,false,mp);
    ix=glGetUniformLocation(prog_id,"m_view");       glUniformMatrix4fv(ix,1,false,mv);
    ix=glGetUniformLocation(prog_id,"m_model");

    // sun
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(1.0,1.0,0.0); glVertex4f(0.0,0.0,0.0,rs); glEnd();
    // planet
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glRotatef(a0,0.0,0.0,1.0);
    glTranslatef(R0,0.0,0.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,m0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.0,0.7,1.0); glVertex4f(0.0,0.0,0.0,r0); glEnd();
    // moon
    glLoadMatrixf(m0);
    glRotatef(a1,0.0,0.0,1.0);
    glTranslatef(R1,0.0,0.0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.4,0.4,0.4); glVertex4f(0.0,0.0,0.0,r1); glEnd();
    // moon
    glLoadMatrixf(m0);
    glRotatef(a2,0.0,0.0,1.0);
    glTranslatef(R2,0.0,0.0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.4,0.4,0.4); glVertex4f(0.0,0.0,0.0,r2); glEnd();
    // planet
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glRotatef(a3,0.0,0.0,1.0);
    glTranslatef(R3,0.0,0.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,m0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.0,0.7,1.0); glVertex4f(0.0,0.0,0.0,r3); glEnd();
    // moon
    glLoadMatrixf(m0);
    glRotatef(a4,0.0,0.0,1.0);
    glTranslatef(R4,0.0,0.0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.4,0.4,0.4); glVertex4f(0.0,0.0,0.0,r4); glEnd();
    // moon
    glLoadMatrixf(m0);
    glRotatef(a5,0.0,0.0,1.0);
    glTranslatef(R5,0.0,0.0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.4,0.4,0.4); glVertex4f(0.0,0.0,0.0,r5); glEnd();

    glUseProgram(0);

    glFlush();
    SwapBuffers(hdc);
    }
//---------------------------------------------------------------------------
void __fastcall TForm1::Timer1Timer(TObject *Sender)
    {
    // this is periodicaly called by timer
    gl_draw();
    float dt=0.001*float(Timer1->Interval); // timer period in seconds
    a0=fmod(a0+da0*dt,360.0);
    a1=fmod(a1+da1*dt,360.0);
    a3=fmod(a3+da3*dt,360.0);
    a4=fmod(a4+da4*dt,360.0);
    a5=fmod(a5+da5*dt,360.0);
    b =fmod(b +db *dt,360.0);
    }
//---------------------------------------------------------------------------

我得到了這個 output （使用我的球體着色器）：

着色器只需將點x,y,z,r作為球體 3D 中心和半徑，發射 BBOX 四邊形並使用正常着色渲染內接球體。 它還使用顏色和您的 3 個矩陣。

因此，如果我認為正確，您應該執行以下操作：

model = identity; 
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render star
model = identity; 
model = glm::rotate(model, glm::radians(a0), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R0, 0.0, 0.0));
model0= model;
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render planet
model = model0;
model = glm::rotate(model, glm::radians(a1), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R1, 0.0, 0.0));
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render moon
model = model0;
model = glm::rotate(model, glm::radians(a2), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R2, 0.0, 0.0));
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render moon
model = identity; 
model = glm::rotate(model, glm::radians(a3), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R3, 0.0, 0.0));
model0= model;
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render planet
model = model0;
model = glm::rotate(model, glm::radians(a4), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R4, 0.0, 0.0));
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render moon
model = model0;
model = glm::rotate(model, glm::radians(a5), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R5, 0.0, 0.0));
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render moon

如果這不起作用，那么您在矩陣順序和使用的數學之間會出現其他不匹配，或者 GLM 的行為與我預期的不同。 我使用普通角度進行自旋轉，所以你只需為你的身體添加索引......

還要注意舊的 GL 旋轉使用[deg]所以如果 GLM 想要[rad]你需要轉換角度和 angular 速度常數......

如果您想要更精確/與現實世界相關的東西或更好地直觀地看到這個：

• 是否有可能在大小和質量方面進行逼真的 n 體太陽系模擬？

Answer 2

object A 繞 B 旋轉順序：A 自旋轉，平移到 A 到 B 的偏移，繞 B 旋轉，平移 B position。 由於 B 是我假設在您的世界起源的太陽，並且一切都在 xz 平面上（笛卡爾坐標不是 OpenGL 坐標），因此變為：

model = glm::rotate(identity, glm::radians(-100.0f * time), glm::vec3(1.0, 0.0, 0.0)); //self-rotation
model = glm::translate(model, glm::vec3(8.0, 0.0, 0.0)); // earth is 8 away from sun, where unrotated about sun is 8 units east
model = glm::rotate(model, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0)); //rotate about sun
// no need for another translation since sun is at origin

然后對於父級為地球的 object，您首先解決該關系，然后再解析父級到世界的關系：

model = glm::rotate(identity, glm::radians(-100.0f * time), glm::vec3(1.0, 0.0, 0.0)); //self-rotation of moon
model = glm::translate(model, glm::vec3(-4.0, 0.0, 0.0)); // moon is 4 away from Earth, where unrotated about Earth is 4 units west
model = glm::rotate(model, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0)); //rotate about Earth
// translate to Earth origin, which is calculate from above code block

免責聲明，我沒有使用glm-math，這只是幾何變換的順序，不知道是不是直接轉化為glm::x

Answer 3

你能做這個項目嗎？？？