first commit

Author: Ushio

.gitignore

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+build
+bin/*

.gitmodules

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+[submodule "libs/prlib"]
+	path = libs/prlib
+	url = https://github.com/Ushio/prlib

README.md

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+## Cone TightFit AABB
+
+Thanks 
+http://iquilezles.org/www/articles/diskbbox/diskbbox.htm
+
+```
+
+git submodule update --init
+premake5 vs2019
+
+```
+
+## demo
+![image](demo.gif)
+![image](idea.png)
+![image](form.png)
+
+<!-- 
+a=\begin{pmatrix} x_{ T } \\ y_{ T } \\ z_{ T } \end{pmatrix}=P_{ 1 }-P_{ 0 }\\ \overrightarrow { x } =\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix},\overrightarrow { y } =\begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix},\overrightarrow { z } =\begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}\\ \overrightarrow { x } \times a=\begin{pmatrix} y_{ 1 }z_{ 2 }-z_{ 1 }y_{ 2 } \\ z_{ 1 }x_{ 2 }-x_{ 1 }z_{ 2 } \\ x_{ 1 }y_{ 2 }-y_{ 1 }x_{ 2 } \end{pmatrix}=\begin{pmatrix} 0z_{ 2 }-0y_{ 2 } \\ 0x_{ 2 }-1z_{ 2 } \\ 1y_{ 2 }-0x_{ 2 } \end{pmatrix}=\begin{pmatrix} 0 \\ -z_{ T } \\ y_{ T } \end{pmatrix}\\ \left\| \overrightarrow { x } \times a \right\| =\sqrt { { z_{ T } }^{ 2 }+{ y_{ T } }^{ 2 } } \\ \left\| \overrightarrow { x } \times \frac { a }{ \left\| a \right\|  }  \right\| =\frac { 1 }{ \left\| a \right\|  } \sqrt { { z_{ T } }^{ 2 }+{ y_{ T } }^{ 2 } } =\sqrt { \frac { 1 }{ { \left\| a \right\|  }^{ 2 } } \left( { z_{ T } }^{ 2 }+{ y_{ T } }^{ 2 } \right)  } \\ \\ { x_{ T } }^{ 2 }+{ y_{ T } }^{ 2 }+{ z_{ T } }^{ 2 }={ \left\| a \right\|  }^{ 2 }\\ { y_{ T } }^{ 2 }+{ z_{ T } }^{ 2 }={ \left\| a \right\|  }^{ 2 }-{ x_{ T } }^{ 2 }\\ \left\| \overrightarrow { x } \times \frac { a }{ \left\| a \right\|  }  \right\| =\sqrt { \frac { 1 }{ { \left\| a \right\|  }^{ 2 } } \left( { \left\| a \right\|  }^{ 2 }-{ x_{ T } }^{ 2 } \right)  } =\sqrt { 1-\frac { { x_{ T } }^{ 2 } }{ { \left\| a \right\|  }^{ 2 } }  } \\ \\ \overrightarrow { y } \times a=\begin{pmatrix} y_{ 1 }z_{ 2 }-z_{ 1 }y_{ 2 } \\ z_{ 1 }x_{ 2 }-x_{ 1 }z_{ 2 } \\ x_{ 1 }y_{ 2 }-y_{ 1 }x_{ 2 } \end{pmatrix}=\begin{pmatrix} 1z_{ 2 }-0y_{ 2 } \\ 0x_{ 2 }-0z_{ 2 } \\ 0y_{ 2 }-1x_{ 2 } \end{pmatrix}=\begin{pmatrix} z_{ T } \\ 0 \\ -x_{ T } \end{pmatrix}\\ \left\| \overrightarrow { y } \times a \right\| =\sqrt { { z_{ T } }^{ 2 }+{ x_{ T } }^{ 2 } } \\ \left\| \overrightarrow { y } \times \frac { a }{ \left\| a \right\|  }  \right\| =\frac { 1 }{ \left\| a \right\|  } \sqrt { { z_{ T } }^{ 2 }+{ x_{ T } }^{ 2 } } =\sqrt { \frac { 1 }{ { \left\| a \right\|  }^{ 2 } } \left( { z_{ T } }^{ 2 }+{ x_{ T } }^{ 2 } \right)  } \\ =\sqrt { \frac { 1 }{ { \left\| a \right\|  }^{ 2 } } \left( { \left\| a \right\|  }^{ 2 }-{ y_{ T } }^{ 2 } \right)  } =\sqrt { 1-\frac { { y_{ T } }^{ 2 } }{ { \left\| a \right\|  }^{ 2 } }  } \\ \\ \overrightarrow { z } \times a=\begin{pmatrix} y_{ 1 }z_{ 2 }-z_{ 1 }y_{ 2 } \\ z_{ 1 }x_{ 2 }-x_{ 1 }z_{ 2 } \\ x_{ 1 }y_{ 2 }-y_{ 1 }x_{ 2 } \end{pmatrix}=\begin{pmatrix} 0z_{ 2 }-1y_{ 2 } \\ 1x_{ 2 }-0z_{ 2 } \\ 0y_{ 2 }-0x_{ 2 } \end{pmatrix}=\begin{pmatrix} -y_{ T } \\ x_{ T } \\ 0 \end{pmatrix}\\ \left\| \overrightarrow { z } \times \frac { a }{ \left\| a \right\|  }  \right\| =\frac { 1 }{ \left\| a \right\|  } \sqrt { { x_{ T } }^{ 2 }+{ y_{ T } }^{ 2 } } =\sqrt { \frac { 1 }{ { \left\| a \right\|  }^{ 2 } } \left( { x_{ T } }^{ 2 }+{ y_{ T } }^{ 2 } \right)  } \\ =\sqrt { \frac { 1 }{ { \left\| a \right\|  }^{ 2 } } \left( { \left\| a \right\|  }^{ 2 }-{ z_{ T } }^{ 2 } \right)  } =\sqrt { 1-\frac { { z_{ T } }^{ 2 } }{ { \left\| a \right\|  }^{ 2 } }  } \\ \overrightarrow { e } =\begin{pmatrix} \sqrt { 1-\frac { { x_{ T } }^{ 2 } }{ a\cdot a }  }  \\ \sqrt { 1-\frac { { y_{ T } }^{ 2 } }{ a\cdot a }  }  \\ \sqrt { 1-\frac { { z_{ T } }^{ 2 } }{ a\cdot a }  }  \end{pmatrix}\\ 
+
+ -->
+
+
+
+

demo.gif

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+#include "pr.hpp"
+#include <iostream>
+#include <memory>
+
+int main() {
+    using namespace pr;
+
+    Config config;
+    config.ScreenWidth = 1920;
+    config.ScreenHeight = 1080;
+    config.SwapInterval = 1;
+    Initialize(config);
+
+    Camera3D camera;
+    camera.origin = { 4, 8, 8 };
+    camera.lookat = { 0, 0, 0 };
+    camera.zUp = false;
+
+    double e = GetElapsedTime();
+
+	glm::vec3 p0 = { -2, 2, -3 };
+	glm::vec3 p1 = { 2, 5, 1 };
+	float r0 = 0.5f;
+	float r1 = 1.0f;
+
+    while (pr::NextFrame() == false) {
+        if (IsImGuiUsingMouse() == false) {
+            UpdateCameraBlenderLike(&camera);
+        }
+
+        ClearBackground(0.1f, 0.1f, 0.1f, 1);
+
+        BeginCamera(camera);
+
+        PushGraphicState();
+
+        DrawGrid(GridAxis::XZ, 1.0f, 10, { 128, 128, 128 });
+        DrawXYZAxis(1.0f);
+
+		DrawTube(p0, p1, r0, r1, {255, 255, 0}, 32);
+
+		glm::vec3 a = p1 - p0;
+		glm::vec3 e = glm::sqrt(
+			glm::max(
+				glm::vec3(1.0f) - a * a / glm::dot(a, a),
+				glm::vec3(0.0f)
+			)
+		);
+
+		glm::vec3 lower = glm::min(p0 - e * r0, p1 - e * r1);
+		glm::vec3 upper = glm::max(p0 + e * r0, p1 + e * r1);
+		DrawAABB(lower, upper, {255, 255, 255}, 2);
+
+        ManipulatePosition(camera, &p0, 0.5f);
+        ManipulatePosition(camera, &p1, 0.5f);
+
+        PopGraphicState();
+        EndCamera();
+
+        BeginImGui();
+
+        ImGui::SetNextWindowSize({ 500, 800 }, ImGuiCond_Once);
+        ImGui::Begin("Panel");
+		ImGui::Text("fps = %f", GetFrameRate());
+        ImGui::SliderFloat("perspective", &camera.perspective, 0, 1);
+        ImGui::SliderFloat("r1", &r0, 0, 1);
+        ImGui::SliderFloat("r2", &r1, 0, 1);
+
+        ImGui::End();
+
+        EndImGui();
+    }
+
+    pr::CleanUp();
+}

form.png

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+include "libs/PrLib"
+
+workspace "ConeTightFitAABB"
+    location "build"
+    configurations { "Debug", "Release" }
+    startproject "main"
+
+architecture "x86_64"
+
+externalproject "prlib"
+	location "libs/PrLib/build" 
+    kind "StaticLib"
+    language "C++"
+
+project "main"
+    kind "ConsoleApp"
+    language "C++"
+    targetdir "bin/"
+    systemversion "latest"
+    flags { "MultiProcessorCompile", "NoPCH" }
+
+    -- Src
+    files { "main.cpp" }
+    
+    -- prlib
+    -- setup command
+    -- git submodule add https://github.com/Ushio/prlib libs/prlib
+    -- premake5 vs2017
+    dependson { "prlib" }
+    includedirs { "libs/prlib/src" }
+    libdirs { "libs/prlib/bin" }
+    filter {"Debug"}
+        links { "prlib_d" }
+    filter {"Release"}
+        links { "prlib" }
+    filter{}
+
+    symbols "On"
+
+    filter {"Debug"}
+        runtime "Debug"
+        targetname ("Main_Debug")
+        optimize "Off"
+    filter {"Release"}
+        runtime "Release"
+        targetname ("Main")
+        optimize "Full"
+    filter{}