Math

引言

上一节我们为引擎提供了自己的键鼠映射，今天我们来聊聊之后的渲染部分的数学基础。

渲染是非常依赖数学的，所以如果想在屏幕上画些什么我们必须拥有一个数学库。

老实说现在有许多优秀的第三方数学库，在我的专业工作中也常常用到。从技术上讲，自己编写的数学库维持最低限度的启动和运行实际上并不难，你可能会编写基础的类如向量、矩阵等等；显然它也需要一些实用方法如基本的运算。

自己做起来很容易，但是如果您想编写一个好的数学库是非常困难的。因为为了使运算快速、为了以一种高效的方式编写它，我们需要非常特殊的编程技巧或者底层功底（涉及到寄存器和汇编代码）。

GLM 库

遗憾的是对于这个系列而言我们谈论的大多是 C++，如何建立一个高效数学库并不在我们的考量范围内。因此我们会使用称为 OpenGL Mathematics（简称 glm）的支持库：

• https://glm.g-truc.net/0.9.9/index.html

它是一个用于图形的 C++ 数学库，虽然名字带着 OpenGL，但请注意它与 OpenGL 无关，只是语法近似于 OpenGL 的数学库。

现在让我们引入该库：

cd Infinite
git submodule add https://github.com/g-truc/glm Infinite/vendor/glm

预生成文件

在项目 Infinite 的预生成文件 premake5.lua 中加入 glm：

workspace "Infinite"
  architecture "x64"
  startproject "Sandbox"

  configurations
  {
    "Debug",
    "Release",
    "Dist"
  }

outputdir = "%{cfg.buildcfg}-%{cfg.system}-%{cfg.architecture}"

-- Include directories relative to root folder (solution directory)
IncludeDir = {}
IncludeDir["GLFW"] = "Infinite/vendor/GLFW/include"
IncludeDir["GLAD"] = "Infinite/vendor/GLAD/include"
IncludeDir["ImGui"] = "Infinite/vendor/imgui/include"
+IncludeDir["glm"] = "Infinite/vendor/glm"

include "Infinite/vendor/GLFW"
include "Infinite/vendor/GLAD"
include "Infinite/vendor/imgui"

project "Infinite"
  location "Infinite"
  kind "SharedLib"
  language "C++"
  staticruntime "off"

  targetdir ("bin/" .. outputdir .. "/%{prj.name}")
  objdir ("bin-int/" .. outputdir .. "/%{prj.name}")

  pchheader "ifnpch.h"
  pchsource "Infinite/src/ifnpch.cpp"

  files
  {
    "%{prj.name}/src/**.h",
    "%{prj.name}/src/**.cpp",
+   "%{prj.name}/vendor/glm/glm/**.hpp",
+   "%{prj.name}/vendor/glm/glm/**.inl",
  }

  includedirs
  {
    "%{prj.name}/src",
    "%{prj.name}/vendor/spdlog/include",
    "%{IncludeDir.GLFW}",
    "%{IncludeDir.GLAD}",
    "%{IncludeDir.ImGui}",
+   "%{IncludeDir.glm}"
  }

  links
  {
    "GLFW",
    "GLAD",
    "ImGui",
    "opengl32.lib"
  }

  filter "system:windows"
    cppdialect "C++17"
    systemversion "latest"

    defines
    {
      "IFN_PLATFORM_WINDOWS",
      "IFN_BUILD_DLL",
      "GLFW_INCLUDE_NONE"
    }

    postbuildcommands
    {
      ("{COPY} %{cfg.buildtarget.relpath} \"../bin/" .. outputdir .. "/Sandbox/\"")
    }

  filter "configurations:Debug"
      defines "IFN_DEBUG"
      runtime "Debug"
      symbols "On"

  filter "configurations:Release"
      defines "IFN_RELEASE"
      runtime "Release"
      optimize "On"

  filter "configurations:Dist"
      defines "IFN_DIST"
      runtime "Release"
      optimize "On"



project "Sandbox"
  location "Sandbox"
  kind "ConsoleApp"
  staticruntime "off"

  language "C++"

  targetdir ("bin/" .. outputdir .. "/%{prj.name}")
  objdir ("bin-int/" .. outputdir .. "/%{prj.name}")

  files
  {
    "%{prj.name}/src/**.h",
    "%{prj.name}/src/**.cpp"
  }

  includedirs
  {
    "Infinite/vendor/spdlog/include",
    "Infinite/src/Infinite",
    "Infinite/src/Events",
    "Infinite/src/**.h",
    "Infinite/src/**.cpp",
+   "%{IncludeDir.glm}"
  }

  links
  {
    "Infinite"
  }

  filter "system:windows"
    cppdialect "C++17"
    systemversion "latest"

    defines
    {
      "IFN_PLATFORM_WINDOWS"
    }

  filter "configurations:Debug"
      defines "IFN_DEBUG"
      runtime "Debug"
      symbols "On"

  filter "configurations:Release"
      defines "IFN_RELEASE"
      runtime "Release"
      optimize "On"

  filter "configurations:Dist"
      defines "IFN_DIST"
      runtime "Release"
      optimize "On"

重新生成项目后打开 VisualStudio，在 vendor 下可以看到 glm：

所有的 .hpp 和 .inl 文件都显示可用：

调试

我们在 SandboxApp.cpp 中放置一段 glm 示例代码：

#include <glm/vec3.hpp> // glm::vec3
#include <glm/vec4.hpp> // glm::vec4
#include <glm/mat4x4.hpp> // glm::mat4
#include <glm/gtc/matrix_transform.hpp> // glm::translate, glm::rotate, glm::scale, glm::perspective
glm::mat4 camera(float Translate, glm::vec2 const & Rotate)
{
    glm::mat4 Projection = glm::perspective(glm::radians(45.0f), 4.0f / 3.0f, 0.1f, 100.f);
    glm::mat4 View = glm::translate(glm::mat4(1.0f), glm::vec3(0.0f, 0.0f, -Translate));
    View = glm::rotate(View, Rotate.y, glm::vec3(-1.0f, 0.0f, 0.0f));
    View = glm::rotate(View, Rotate.x, glm::vec3(0.0f, 1.0f, 0.0f));
    glm::mat4 Model = glm::scale(glm::mat4(1.0f), glm::vec3(0.5f));
    return Projection * View * Model;
}

#include <Infinite.h>

+#include <glm/vec3.hpp> // glm::vec3
+#include <glm/vec4.hpp> // glm::vec4
+#include <glm/mat4x4.hpp> // glm::mat4
+#include <glm/gtc/matrix_transform.hpp> // glm::translate, glm::rotate, glm::scale, glm::perspective
+glm::mat4 camera(float Translate, glm::vec2 const & Rotate)
+{
+   glm::mat4 Projection = glm::perspective(glm::radians(45.0f), 4.0f / 3.0f, 0.1f, 100.f);
+   glm::mat4 View = glm::translate(glm::mat4(1.0f), glm::vec3(0.0f, 0.0f, -Translate));
+   View = glm::rotate(View, Rotate.y, glm::vec3(-1.0f, 0.0f, 0.0f));
+   View = glm::rotate(View, Rotate.x, glm::vec3(0.0f, 1.0f, 0.0f));
+   glm::mat4 Model = glm::scale(glm::mat4(1.0f), glm::vec3(0.5f));
+   return Projection * View * Model;
+}


class ExampleLayer : public Infinite::Layer
{
public:
	ExampleLayer()
		: Layer("Example")
	{
+		auto cam = camera(5.0f, { 0.5f, 0.5f });
	}

	void OnUpdate() override
	{
		// IFN_INFO("ExampleLayer::Update");

		if (Infinite::Input::IsKeyPressed(IFN_KEY_TAB))
			IFN_INFO("Tab key is pressed (poll)!");
	}

	void OnEvent(Infinite::Event& event) override
	{
			if (event.GetEventType() == Infinite::EventType::KeyPressed)
			{
				Infinite::KeyPressedEvent& e = (Infinite::KeyPressedEvent&)event;
				if (Infinite::Input::IsKeyPressed(IFN_KEY_TAB))
					IFN_INFO("Tab key is pressed (event)!");

				IFN_TRACE("{0}", (char)e.GetKeyCode());
			} 
	}

};

class Sandbox : public Infinite::Application {
public:
	Sandbox() 
	{
		PushLayer(new ExampleLayer());
		PushOverlay(new Infinite::ImGuiLayer());
	}
	~Sandbox() {}
};

Infinite::Application* Infinite::CreateApplication() {
	return new Sandbox();
}

加入示例代码后如成功启动则代表引入成功，测试完毕删除示例代码。