Introduction to 3D Game Programming with DirectX 12 学习笔记之 --- 第十五章：第一人称摄像机和动态索引

原文:Introduction to 3D Game Programming with DirectX 12 学习笔记之 --- 第十五章：第一人称摄像机和动态索引

代码工程地址：

https://github.com/jiabaodan/Direct12BookReadingNotes

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学习目标

1. 回顾视景坐标系变换的数学算法；
2. 熟悉第一人称摄像机的功能；
3. 实现第一人称摄像机；
4. 理解如何动态索引一组纹理。

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1 回顾视景坐标系变换

如果QW = (Qx, Qy, Qz, 1), uW = (ux, uy, uz, 0), vW = (vx, vy, vz, 0)并且wW = (wx, wy, wz, 0)。根据第三章4.3节，我们可以知道从视景坐标系变化到世界坐标系的变换矩阵为：



根据第三章4.5节，我们需要的是它的逆矩阵。因为世界坐标系和视景坐标系只变换位置和旋转，所以：





所以视景坐标系变换矩阵为：

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2 摄像机类

为了封装摄像机相关的代码，我们封装和实现了一个Camera类。它的数据主要分为下面几类：位置，右向，向上的向量和看向的向量；原点，视景坐标系在世界坐标系下的xyz轴：

class Camera
{
public:
	Camera();
	˜Camera();

	// Get/Set world camera position.
	DirectX::XMVECTOR GetPosition()const;
	DirectX::XMFLOAT3 GetPosition3f()const;
	void SetPosition(float x, float y, float z);
	void SetPosition(const DirectX::XMFLOAT3& v);

	// Get camera basis vectors.
	DirectX::XMVECTOR GetRight()const;
	DirectX::XMFLOAT3 GetRight3f()const;
	DirectX::XMVECTOR GetUp()const;
	DirectX::XMFLOAT3 GetUp3f()const;
	DirectX::XMVECTOR GetLook()const;
	DirectX::XMFLOAT3 GetLook3f()const;

	// Get frustum properties.
	float GetNearZ()const;
	float GetFarZ()const;
	float GetAspect()const;
	float GetFovY()const;
	float GetFovX()const;

	// Get near and far plane dimensions in view space coordinates.
	float GetNearWindowWidth()const;
	float GetNearWindowHeight()const;
	float GetFarWindowWidth()const;
	float GetFarWindowHeight()const;

	// Set frustum.
	void SetLens(float fovY, float aspect, float zn, float zf);

	// Define camera space via LookAt parameters.
	void LookAt(DirectX::FXMVECTOR pos,
	DirectX::FXMVECTOR target,
	DirectX::FXMVECTOR worldUp);
	void LookAt(const DirectX::XMFLOAT3& pos,
	const DirectX::XMFLOAT3& target,
	const DirectX::XMFLOAT3& up);

	// Get View/Proj matrices.
	DirectX::XMMATRIX GetView()const;
	DirectX::XMMATRIX GetProj()const;
	DirectX::XMFLOAT4X4 GetView4x4f()const;
	DirectX::XMFLOAT4X4 GetProj4x4f()const;

	// Strafe/Walk the camera a distance d.
	void Strafe(float d);
	void Walk(float d);

	// Rotate the camera.
	void Pitch(float angle);
	void RotateY(float angle);

	// After modifying camera position/orientation, call to rebuild the view matrix.
	void UpdateViewMatrix();

private:
	// Camera coordinate system with coordinates relative to world space.
	DirectX::XMFLOAT3 mPosition = { 0.0f, 0.0f, 0.0f };
	DirectX::XMFLOAT3 mRight = { 1.0f, 0.0f, 0.0f };
	DirectX::XMFLOAT3 mUp = { 0.0f, 1.0f, 0.0f };
	DirectX::XMFLOAT3 mLook = { 0.0f, 0.0f, 1.0f };

	// Cache frustum properties.
	float mNearZ = 0.0f;
	float mFarZ = 0.0f;
	float mAspect = 0.0f;
	float mFovY = 0.0f;
	float mNearWindowHeight = 0.0f;
	float mFarWindowHeight = 0.0f;
	bool mViewDirty = true;

	// Cache View/Proj matrices.
	DirectX::XMFLOAT4X4 mView = MathHelper::Identity4x4();
	DirectX::XMFLOAT4X4 mProj = MathHelper::Identity4x4();
};

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3 选择一些方法实现

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3.1 返回XMVECTOR变量

我们提供了一些返回XMVECTOR变量的方法，这个只是为了方便：

XMVECTOR Camera::GetPosition()const
{
	return XMLoadFloat3(&mPosition);
}
XMFLOAT3 Camera::GetPosition3f()const
{
	return mPosition;
}

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3.2 SetLens

我们通过SetLens函数来设置视锥体：

void Camera::SetLens(float fovY, float aspect, float zn, float zf)
{
	// cache properties
	mFovY = fovY;
	mAspect = aspect;
	mNearZ = zn;
	mFarZ = zf;

	mNearWindowHeight = 2.0f * mNearZ * tanf(0.5f*mFovY );
	mFarWindowHeight = 2.0f * mFarZ * tanf(0.5f*mFovY );
	XMMATRIX P = XMMatrixPerspectiveFovLH(mFovY, mAspect, mNearZ, mFarZ);
	XMStoreFloat4x4(&mProj, P);
}

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3.3 通过视锥体派生出来的数据

float Camera::GetFovX()const
{
	float halfWidth = 0.5f*GetNearWindowWidth();
	return 2.0f*atan(halfWidth / mNearZ);
}

float Camera::GetNearWindowWidth()const
{
	return mAspect * mNearWindowHeight;
}

float Camera::GetNearWindowHeight()const
{
	return mNearWindowHeight;
}

float Camera::GetFarWindowWidth()const
{
	return mAspect * mFarWindowHeight;
}

float Camera::GetFarWindowHeight()const
{
	return mFarWindowHeight;
}

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3.4 变换摄像机

对于一个第一人称摄像机，如果无视碰撞检测，我们希望：

1. 向看向的方向前进或者后退；
2. 左右移动；
3. 向上下旋转；
4. 左右旋转。

void Camera::Walk(float d)
{
	// mPosition += d*mLook
	XMVECTOR s = XMVectorReplicate(d);
	XMVECTOR l = XMLoadFloat3(&mLook);
	XMVECTOR p = XMLoadFloat3(&mPosition);
	XMStoreFloat3(&mPosition, XMVectorMultiplyAdd(s, l, p));
}

void Camera::Strafe(float d)
{
	// mPosition += d*mRight
	XMVECTOR s = XMVectorReplicate(d);
	XMVECTOR r = XMLoadFloat3(&mRight);
	XMVECTOR p = XMLoadFloat3(&mPosition);
	XMStoreFloat3(&mPosition, XMVectorMultiplyAdd(s, r, p));
}

void Camera::Pitch(float angle)
{
	// Rotate up and look vector about the right vector.
	XMMATRIX R = XMMatrixRotationAxis(XMLoadFloat3(&mRight), angle);
	XMStoreFloat3(&mUp, XMVector3TransformNormal(XMLoadFloat3(&R));
	XMStoreFloat3(&mLook, XMVector3TransformNormal(XMLoadFloat3(&mLook), R));
}

void Camera::RotateY(float angle)
{
	// Rotate the basis vectors about the world yaxis.
	XMMATRIX R = XMMatrixRotationY(angle);
	XMStoreFloat3(&mRight, XMVector3TransformNormal(XMLoadFloat3(&R));
	XMStoreFloat3(&mUp, XMVector3TransformNormal(XMLoadFloat3(&mUp), R));
	XMStoreFloat3(&mLook, XMVector3TransformNormal(XMLoadFloat3(&mLook), R));
}

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3.5 创建视景坐标系变换矩阵

UpdateViewMatrix函数的第一部分是重新标准正交化摄像机的向右，向上和看向的向量。因为经过变换后，由于数值问题可能导致它们不再标准正交；第二部分就是计算矩阵：

void Camera::UpdateViewMatrix()
{
	if(mViewDirty)
	{
		XMVECTOR R = XMLoadFloat3(&mRight);
		XMVECTOR U = XMLoadFloat3(&mUp);
		XMVECTOR L = XMLoadFloat3(&mLook);
		XMVECTOR P = XMLoadFloat3(&mPosition);

		// Keep camera’s axes orthogonal to each other and of unit length.
		L = XMVector3Normalize(L);
		U = XMVector3Normalize(XMVector3Cross(L, R));

		// U, L already ortho-normal, so no need to normalize cross product.
		R = XMVector3Cross(U, L);

		// Fill in the view matrix entries.
		float x = -XMVectorGetX(XMVector3Dot(P, R));
		float y = -XMVectorGetX(XMVector3Dot(P, U));
		float z = -XMVectorGetX(XMVector3Dot(P, L));

		XMStoreFloat3(&mRight, R);
		XMStoreFloat3(&mUp, U);
		XMStoreFloat3(&mLook, L);
		mView(0, 0) = mRight.x;
		mView(1, 0) = mRight.y;
		mView(2, 0) = mRight.z;
		mView(3, 0) = x;
		mView(0, 1) = mUp.x;
		mView(1, 1) = mUp.y;
		mView(2, 1) = mUp.z;
		mView(3, 1) = y;
		mView(0, 2) = mLook.x;
		mView(1, 2) = mLook.y;
		mView(2, 2) = mLook.z;
		mView(3, 2) = z;
		mView(0, 3) = 0.0f;
		mView(1, 3) = 0.0f;
		mView(2, 3) = 0.0f;
		mView(3, 3) = 1.0f;
		mViewDirty = false;
	}
}

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4 摄像机Demo注释

我们删除以前老的摄像机相关的变量mPhi, mTheta, mRadius, mView, 和mProj，添加新的变量：

Camera mCam;

然后在屏幕尺寸变化的时候，不再直接计算透视矩阵，而是SetLens：

void CameraApp::OnResize()
{
	D3DApp::OnResize();
	mCamera.SetLens(0.25f*MathHelper::Pi, AspectRatio(), 1.0f, 1000.0f);
}

在UpdateScene方法中：

void CameraApp::UpdateScene(float dt)
{
	if( GetAsyncKeyState(‘W’) & 0x8000 )
		mCamera.Walk(10.0f*dt);
	if( GetAsyncKeyState(‘S’) & 0x8000 )
		mCamera.Walk(-10.0f*dt);
	if( GetAsyncKeyState(‘A’) & 0x8000 )
		mCamera.Strafe(-10.0f*dt);
	if( GetAsyncKeyState(‘D’) & 0x8000 )
		mCamera.Strafe(10.0f*dt);

在OnMouseMove方法中：

void CameraAndDynamicIndexingApp::OnMouseMove(WPARAM btnState, int x, int y)
{
	if( (btnState & MK_LBUTTON) != 0 )
	{
		// Make each pixel correspond to a quarter of a degree.
		float dx = XMConvertToRadians(0.25f*static_cast<float>(x - mLastMousePos.x));
		float dy = XMConvertToRadians(0.25f*static_cast<float>(y - mLastMousePos.y));

		mCamera.Pitch(dy);
		mCamera.RotateY(dx);
	}

	mLastMousePos.x = x;
	mLastMousePos.y = y;
}

最终，视景和透视投影矩阵可以通过摄像机实例访问：

mCamera.UpdateViewMatrix();

XMMATRIX view = mCamera.View();
XMMATRIX proj = mCamera.Proj();

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5 动态索引

动态索引的思路非常简单，我们在着色器程序中动态索引一组资源，本Demo中，资源是一组纹理。索引可以通过多种方法定义：

1. 可以是常量缓冲中的一个元素；
2. 可以是一个系统ID：SV_PrimitiveID, SV_VertexID, SV_DispatchThreadID, or SV_InstanceID；
3. 可以是通过计算得到的结果；
4. 可以是纹理中的值；
5. 可以是顶点结构中的组件。

下面是一个常量缓冲中的索引例子：

cbuffer cbPerDrawIndex : register(b0)
{
	int gDiffuseTexIndex;
};

Texture2D gDiffuseMap[4] : register(t0);
float4 texValue = gDiffuseMap[gDiffuseTexIndex].Sample(gsamLinearWrap, pin.TexC);

对于当前Demo，我们的目标是：最小化我们每帧设置的descriptors的数量。我们设置物体的常量缓冲，材质常量缓冲和和漫反射问题贴图。最小化descriptors可以让我们的根签名更小，这代表每个绘制调用造成更少的性能开销；并且这个技术对实例化技术非常有用（下章讲解），我们的策略如下：

1. 创建一个结构化缓冲保存所有的材质数据；
2. 在物体常量缓冲中添加一个MaterialIndex值来指定使用的材质的索引；
3. 绑定所有SRV descriptors每帧一次（之前每个渲染物体绑定一次）；
4. 在材质数据中添加DiffuseMapIndex值来指定使用的纹理贴图。

根据上面的设置，我们只需要对每个渲染物体设置逐物体的常量缓冲。然后使用MaterialIndex来匹配材质，使用DiffuseMapIndex来匹配纹理。

struct MaterialData
{
	DirectX::XMFLOAT4 DiffuseAlbedo = { 1.0f, 1.0f, 1.0f, 1.0f };
	DirectX::XMFLOAT3 FresnelR0 = { 0.01f, 0.01f, 0.01f };
	float Roughness = 64.0f;

	// Used in texture mapping.
	DirectX::XMFLOAT4X4 MatTransform = MathHelper::Identity4x4();
	UINT DiffuseMapIndex = 0;
	UINT MaterialPad0;
	UINT MaterialPad1;
	UINT MaterialPad2;
};

MaterialBuffer = std::make_unique<UploadBuffer<MaterialData>>(device, materialCount, false);

然后根据着色器，更新根签名：

CD3DX12_DESCRIPTOR_RANGE texTable;
texTable.Init(D3D12_DESCRIPTOR_RANGE_TYPE_SRV, 4, 0, 0);

// Root parameter can be a table, root descriptor or root constants.
CD3DX12_ROOT_PARAMETER slotRootParameter[4];

// Perfomance TIP: Order from most frequent to least frequent.
slotRootParameter[0].InitAsConstantBufferView(0);
slotRootParameter[1].InitAsConstantBufferView(1);
slotRootParameter[2].InitAsShaderResourceView(0, 1);
slotRootParameter[3].InitAsDescriptorTable(1, &texTable, D3D12_SHADER_VISIBILITY_PIXEL);
auto staticSamplers = GetStaticSamplers();

// A root signature is an array of root parameters.
CD3DX12_ROOT_SIGNATURE_DESC rootSigDesc(4,
	slotRootParameter,
	(UINT)staticSamplers.size(),
	staticSamplers.data(),
	D3D12_ROOT_SIGNATURE_FLAG_ALLOW_INPUT_ASSEMBLER_INPUT_

现在，绘制任何渲染物体之前，我们可以绑定所有材质和纹理SRV每帧一次：

void CameraAndDynamicIndexingApp::Draw(const GameTimer& gt)
{
	…
	auto passCB = mCurrFrameResource->PassCB->Resource();
	mCommandList->SetGraphicsRootConstantBufferView(1, passCB->GetGPUVirtualAddress());

	// Bind all the materials used in this scene. For structured buffers,
	// we can bypass the heap and set as a root descriptor.
	auto matBuffer = mCurrFrameResource->MaterialBuffer->Resource();
	mCommandList->SetGraphicsRootShaderResourceView(2, matBuffer->GetGPUVirtualAddress());

	// Bind all the textures used in this scene. Observe
	// that we only have to specify the first descriptor in the table.
	// The root signature knows how many descriptors are expected in the table.
	mCommandList->SetGraphicsRootDescriptorTable(3,
		mSrvDescriptorHeap->GetGPUDescriptorHandleForHeapStart());

	DrawRenderItems(mCommandList.Get(), mOpaqueRitems);
	…
}

void CameraAndDynamicIndexingApp::DrawRenderItems(
	ID3D12GraphicsCommandList* cmdList,
	const std::vector<RenderItem*>& ritems)
{
	…
	// For each render item…
	for(size_t i = 0; i < ritems.size(); ++i)
	{
		auto ri = ritems[i];
		…
		cmdList->SetGraphicsRootConstantBufferView(0, objCBAddress);
		cmdList->DrawIndexedInstanced(ri->IndexCount, 1,
			ri->StartIndexLocation, ri- >BaseVertexLocation, 0);
	}
}

然后更新ObjectConstants结构（已经添加并更新MaterialIndex）：

// UpdateObjectCBs…
ObjectConstants objConstants;
XMStoreFloat4x4(&objConstants.World, XMMatrixTranspose(world));
XMStoreFloat4x4(&objConstants.TexTransform, XMMatrixTranspose(texTransform));
**objConstants.MaterialIndex = e->Mat->MatCBIndex;**

着色器代码更新：

// Include structures and functions for lighting.
#include “LightingUtil.hlsl”
struct MaterialData
{
	float4 DiffuseAlbedo;
	float3 FresnelR0;
	float Roughness;
	float4x4 MatTransform;
	uint DiffuseMapIndex;
	uint MatPad0;
	uint MatPad1;
	uint MatPad2;
};

// An array of textures, which is only supported in shader model 5.1+. Unlike
// Texture2DArray, the textures in this array can be different sizes and
// formats, making it more flexible than texture arrays.
Texture2D gDiffuseMap[4] : register(t0);

// Put in space1, so the texture array does not overlap with these resources.
// The texture array will occupy registers t0, t1, …, t3 in space0.
StructuredBuffer<MaterialData> gMaterialData : register(t0, space1);

SamplerState gsamPointWrap : register(s0);
SamplerState gsamPointClamp : register(s1);
SamplerState gsamLinearWrap : register(s2);
SamplerState gsamLinearClamp : register(s3);
SamplerState gsamAnisotropicWrap : register(s4);
SamplerState gsamAnisotropicClamp : register(s5);

// Constant data that varies per frame.
cbuffer cbPerObject : register(b0)
{
	float4x4 gWorld;
	float4x4 gTexTransform;
	uint gMaterialIndex;
	uint gObjPad0;
	uint gObjPad1;
	uint gObjPad2;
};

// Constant data that varies per material.
cbuffer cbPass : register(b1)
{
	float4x4 gView;
	float4x4 gInvView;
	float4x4 gProj;
	float4x4 gInvProj;
	float4x4 gViewProj;
	float4x4 gInvViewProj;
	float3 gEyePosW;
	float cbPerObjectPad1;
	float2 gRenderTargetSize;
	float2 gInvRenderTargetSize;
	float gNearZ;
	float gFarZ;
	float gTotalTime;
	float gDeltaTime;
	float4 gAmbientLight;

	// Indices [0, NUM_DIR_LIGHTS) are directional lights;
	// indices [NUM_DIR_LIGHTS, NUM_DIR_LIGHTS+NUM_POINT_LIGHTS) are point lights;
	// indices [NUM_DIR_LIGHTS+NUM_POINT_LIGHTS,
	//
	NUM_DIR_LIGHTS+NUM_POINT_LIGHT+NUM_SPOT_LIGHTS)

	// are spot lights for a maximum of MaxLights per object.
	Light gLights[MaxLights];
};

struct VertexIn
{
	float3 PosL : POSITION;
	float3 NormalL : NORMAL;
	float2 TexC : TEXCOORD;
};

struct VertexOut
{
	float4 PosH : SV_POSITION;
	float3 PosW : POSITION;
	float3 NormalW : NORMAL;
	float2 TexC : TEXCOORD;
};

VertexOut VS(VertexIn vin)
{
	VertexOut vout = (VertexOut)0.0f;

	// Fetch the material data.
	MaterialData matData = gMaterialData[gMaterialIndex];

	// Transform to world space.
	float4 posW = mul(float4(vin.PosL, 1.0f), gWorld);
	vout.PosW = posW.xyz;

	// Assumes nonuniform scaling; otherwise, need to use inverse-transpose
	// of world matrix.
	vout.NormalW = mul(vin.NormalL, (float3x3)gWorld);

	// Transform to homogeneous clip space.
	vout.PosH = mul(posW, gViewProj);

	// Output vertex attributes for interpolation across triangle.
	float4 texC = mul(float4(vin.TexC, 0.0f, 1.0f), gTexTransform);
	vout.TexC = mul(texC, matData.MatTransform).xy;

	return vout;
}

float4 PS(VertexOut pin) : SV_Target
{
	// Fetch the material data.
	MaterialData matData = gMaterialData[gMaterialIndex];

	float4 diffuseAlbedo = matData.DiffuseAlbedo;
	float3 fresnelR0 = matData.FresnelR0;
	float roughness = matData.Roughness;
	uint diffuseTexIndex = matData.DiffuseMapIndex;

	// Dynamically look up the texture in the array.
	diffuseAlbedo *= gDiffuseMap[diffuseTexIndex].Sample(gsamLinearWrap, pin.TexC);

	// Interpolating normal can unnormalize it, so renormalize it.
	pin.NormalW = normalize(pin.NormalW);

	// Vector from point being lit to eye.
	float3 toEyeW = normalize(gEyePosW - pin.PosW);

	// Light terms.
	float4 ambient = gAmbientLight*diffuseAlbedo;
	Material mat = { diffuseAlbedo, fresnelR0, roughness };
	float4 directLight = ComputeDirectLighting(gLights, mat, pin.PosW, pin.NormalW, toEyeW);
	float4 litColor = ambient + directLight;

	// Common convention to take alpha from diffuse albedo.
	litColor.a = diffuseAlbedo.a;

	return litColor;
}

为了总结本章，动态索引三个额外的用途如下：

1. 合并使用不同纹理的网格到一个渲染项目，这样可以在同一个绘制调用中绘制它们。网格可以在顶点结构中保存texture/material属性；
2. 一个rendering-pass中包含多个纹理（纹理有不同的大小和格式）；
3. 使用不用的纹理和材质实例化渲染项目，材质使用SV_InstanceID值作为索引。我们可以在下一章看到例子。

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6 总结

1. 我们通过摄像机的位置和方向来定义相机坐标系；
2. 在相机类中添加透视投影矩阵；
3. 添加前后左右移动，以及上下左右旋转；
4. 动态索引是新的着色器5.1模型的功能，它可以让我们动态索引一组不同大小和格式的纹理。

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7 练习

2、修改摄像机Demo，添加Roll函数，让相机可以围绕前向向量旋转（空战游戏中很有用）：

Camera类添加代码：

void Roll(float angle);				// 添加Roll

void Camera::Roll(float angle)
{
	// Rotate up and look vector about the look vector.

	XMMATRIX R = XMMatrixRotationAxis(XMLoadFloat3(&mLook), angle);

	XMStoreFloat3(&mUp, XMVector3TransformNormal(XMLoadFloat3(&mUp), R));
	XMStoreFloat3(&mRight, XMVector3TransformNormal(XMLoadFloat3(&mRight), R));

	mViewDirty = true;
}

然后主App类中的RollAndBoxes::OnKeyboardInput函数中添加代码：

// 添加Roll
if (GetAsyncKeyState('Q') & 0x8000)
	mCamera.Roll(3.0f*dt);

if (GetAsyncKeyState('E') & 0x8000)
	mCamera.Roll(-3.0f*dt);