一个3D摄像机的设计与实现

这两天学习了3D图形学。独自花了2天时间设计了一个自由移动的DX9的摄像机类。下面我仔细讲述一下我的Camera类是如何完成的。

e3d_camere.h


#ifndef __e3d_camera__
#define __e3d_camera__
#include <d3dx9.h>namespace e3d {class Camera{public:Camera(IDirect3DDevice9* Device = 0):m_right(D3DXVECTOR3(1.f, 0.f, 0.f)),m_up(D3DXVECTOR3(0.f, 1.f, 0.f)),m_look(D3DXVECTOR3(0.f, 0.f, 1.f)),m_position(D3DXVECTOR3(0.f, 0.f, 0.f)),m_aspect(800.f / 600),m_fovY(D3DX_PI*0.25),m_nearZ(1.f),m_farZ(1000.f),m_view(),m_proj(),_Device(0) {D3DXMatrixIdentity(&m_view);_Device = Device;D3DXMATRIX V;D3DXMatrixLookAtLH(&V, &m_position, &m_look, &m_up);//Device->SetTransform(D3DTS_VIEW, &V);D3DXMatrixPerspectiveFovLH(&m_proj,m_fovY, // 90 - degreem_aspect,m_nearZ,m_farZ);}//设置摄像机位置void SetPosition(float x, float y, float z) { m_position.x = x; m_position.y = y; m_position.z = z;}void SetPositionXM(D3DXVECTOR3 pos) {m_position = pos; }//获得摄像位置及朝向相关参数D3DXVECTOR3 GetPosition()  const { return m_position; }D3DXVECTOR3 GetRight()      const { return m_right; }D3DXVECTOR3 GetUp()            const { return m_up; }D3DXVECTOR3 GetLook()     const { return m_look; }D3DXVECTOR3 GetPositionXM() const { return m_position; }D3DXVECTOR3 GetRightXM()    const { return m_right; }D3DXVECTOR3 GetUpXM()      const { return m_up; }D3DXVECTOR3 GetLookXM()       const { return m_look; }//获得投影相关参数float GetNearZ()  const { return m_nearZ; }float GetFarZ()        const { return m_farZ; }float GetFovY()     const { return m_fovY; }float GetFovX()     const { return atan(m_aspect * tan(m_fovY * 0.5f)) * 2.f; }float GetAspect()    const { return m_aspect; }//获得相关矩阵D3DXMATRIX View()             const { return m_view; }D3DXMATRIX Projection()     const { return m_proj; }D3DXMATRIX ViewProjection() const { return m_view * m_proj; }//设置投影相关参数void SetLens(float fovY, float ratioAspect, float nearZ, float farZ){m_fovY = fovY;m_aspect = ratioAspect;m_nearZ = nearZ;m_farZ = farZ;D3DXMatrixPerspectiveFovLH(&m_proj,m_fovY, // 90 - degreem_aspect,m_nearZ,m_farZ);}//通过位置+观察点来设置视角矩阵void LookAtXM(D3DXVECTOR3 pos, D3DXVECTOR3 lookAt, D3DXVECTOR3 worldUp) {D3DXVECTOR3 look, right, up;D3DXVec3Normalize(&look,&(lookAt - pos));D3DXVec3Cross(&right, &worldUp, &worldUp);D3DXVec3Normalize(&right, &right);D3DXVec3Cross(&up, &look, &right);//XMVECTOR right = XMVector3Normalize(XMVector3Cross(worldUp, look));//XMVECTOR up = XMVector3Cross(look, right);m_position = pos;m_right = right;m_up = up;m_look = look;//XMStoreFloat3(&m_position, pos);//XMStoreFloat3(&m_right, right);//XMStoreFloat3(&m_up, up);//XMStoreFloat3(&m_look, look);}void LookAt(D3DXVECTOR3 pos, D3DXVECTOR3 lookAt, D3DXVECTOR3 worldUp) {LookAtXM(pos, lookAt, worldUp);}//基本操作void Walk(float dist)            //前后行走{ D3DXVECTOR3 pos = m_position;D3DXVECTOR3 look = m_look;pos += D3DXVECTOR3(dist * look.x,dist * look.y,dist * look.z);m_position = pos;}void Strafe(float dist)     //左右平移{D3DXVECTOR3 pos = m_position;D3DXVECTOR3 right = m_right;pos += D3DXVECTOR3(dist * right.x, dist * right.y, dist * right.z);m_position = pos;}void Pitch(float angle)       //上下点头{D3DXMATRIX rotation;D3DXMatrixRotationAxis(&rotation, &m_right, angle);D3DXVec3TransformCoord(&m_up, &m_up, &rotation);D3DXVec3TransformCoord(&m_look, &m_look, &rotation);//XMStoreFloat3(&m_up, XMVector3TransformNormal(XMLoadFloat3(&m_up), rotation));//XMStoreFloat3(&m_look, XMVector3TransformNormal(XMLoadFloat3(&m_look), rotation));}void Yaw(float angle)        //上下点头{D3DXMATRIX rotation;D3DXMatrixRotationAxis(&rotation, &m_up, angle);D3DXVec3TransformCoord(&m_right, &m_right, &rotation);D3DXVec3TransformCoord(&m_look, &m_look, &rotation);//XMStoreFloat3(&m_up, XMVector3TransformNormal(XMLoadFloat3(&m_up), rotation));//XMStoreFloat3(&m_look, XMVector3TransformNormal(XMLoadFloat3(&m_look), rotation));}void RotateY(float angle)     //左右插头{//XMMATRIX rotation  = XMMatrixRotationY(angle);D3DXMATRIX rotation;D3DXMatrixRotationY(&rotation, angle);D3DXVec3TransformCoord(&m_right, &m_right, &rotation);D3DXVec3TransformCoord(&m_up, &m_up, &rotation);D3DXVec3TransformCoord(&m_look, &m_look, &rotation);//XMStoreFloat3(&m_right, XMVector3TransformNormal(XMLoadFloat3(&m_right), rotation));//XMStoreFloat3(&m_up, XMVector3TransformNormal(XMLoadFloat3(&m_up), rotation));//XMStoreFloat3(&m_look, XMVector3TransformNormal(XMLoadFloat3(&m_look), rotation));}void UpdateView() {      //更新相关矩阵D3DXVECTOR3 r = m_right;D3DXVECTOR3 u = m_up;D3DXVECTOR3 l = m_look;D3DXVECTOR3 p = m_position;D3DXVec3Cross(&r, &u, &l);D3DXVec3Normalize(&r, &r);D3DXVec3Cross(&u, &l, &r);D3DXVec3Normalize(&u, &u);D3DXVec3Normalize(&l, &l);//r = XMVector3Normalize(XMVector3Cross(u, l));//u = XMVector3Normalize(XMVector3Cross(l, r));//l = XMVector3Normalize(l);float x = -D3DXVec3Dot(&p, &r);float y = -D3DXVec3Dot(&p, &u);float z =- D3DXVec3Dot(&p, &l);//float x = -XMVectorGetX(XMVector3Dot(p, r));//float y = -XMVectorGetX(XMVector3Dot(p, u));//float z = -XMVectorGetX(XMVector3Dot(p, l));m_right = r;m_up = u;m_look = l;m_position = p;//XMStoreFloat3(&m_right, r);//XMStoreFloat3(&m_up, u);//XMStoreFloat3(&m_look, l);//XMStoreFloat3(&m_position, p);m_view(0, 0) = m_right.x; m_view(0, 1) = m_up.x; m_view(0, 2) = m_look.x;   m_view(0, 3) = 0;m_view(1, 0) = m_right.y;    m_view(1, 1) = m_up.y; m_view(1, 2) = m_look.y;   m_view(1, 3) = 0;m_view(2, 0) = m_right.z;    m_view(2, 1) = m_up.z; m_view(2, 2) = m_look.z;   m_view(2, 3) = 0;m_view(3, 0) = x;        m_view(3, 1) = y;  m_view(3, 2) = z;      m_view(3, 3) = 1;}private:D3DXVECTOR3  m_right;            //位置及三个坐标轴参数D3DXVECTOR3 m_up;D3DXVECTOR3    m_look;D3DXVECTOR3  m_position;float    m_aspect;               //投影相关参数float   m_fovY;float    m_nearZ;float   m_farZ;D3DXMATRIX   m_view;             //视角矩阵D3DXMATRIX    m_proj;             //投影矩阵IDirect3DDevice9* _Device;};
}
#endif // !__e3d_camera__

以上是代码。接下来我会简单地阐明Camera涉及到的数学知识。

用以下4种向量可以来描述摄像机

右向量(right vector)
上向量(up vector)
观察向量(look vector)
位置向量(position vector)

所以说摄像机的Walk(前进后退)和Strafe(左右移动)很好解释。仅需要将positon向量加上look或者right向量。这里我的摄像机没有设计向上升。其实同理让positon加上up向量然后通过UpdateView计算出view(视角矩阵即可)。

下面我说一下左右上下旋转视角。

上下点头

通过D3DXMatrixRotationAxis函数与right向量和角度计算出绕right轴旋转的矩阵。然后通过up和look向量与矩阵相乘更新up和look向量

左右摇头

和上下点头类似这里不再赘述。

数学部分：

先平移后旋转。

平移矩阵很简单

1    0    0    0
0    1    0    0
0    0    1    0
-px -py  -pz   1

旋转矩阵通过up look right向量共同求得

rx   ux   dx   0
ry   uy   dy   0
rz   uz   dz   0
0    0    0    1

矩阵相乘得到

m_view(0, 0) = m_right.x;   m_view(0, 1) = m_up.x; m_view(0, 2) = m_look.x;   m_view(0, 3) = 0;m_view(1, 0) = m_right.y;    m_view(1, 1) = m_up.y; m_view(1, 2) = m_look.y;   m_view(1, 3) = 0;m_view(2, 0) = m_right.z;    m_view(2, 1) = m_up.z; m_view(2, 2) = m_look.z;   m_view(2, 3) = 0;m_view(3, 0) = x;        m_view(3, 1) = y;  m_view(3, 2) = z;      m_view(3, 3) = 1;

以上这些为我学习3d打下坚实基础。也设计出一个完整的摄像机类让我对游戏引擎的设计也会收获很多经验。

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一个3D摄像机的设计与实现

e3d_camere.h

上下点头

左右摇头

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