3D Game Programming Projection Ming-Te Chi Department of Computer Science, National Chengchi University 2018

Projection

Multi-view 一般的建模軟體都提供多重視角的畫面，方便理解與建立3D model 從左上順時鐘方向依序為，正面正交投影、下方正交投影，相機視點透視投影和側面視點正交投影

Classical Projections 幾種工程繪圖中常見的透視方法 Angel: Interactive Computer Graphics 5E ©

Eye coordinates +y +y +x +x +z 由於成像是會依相機(觀察者)的位置和角度進行繪圖， 故整體來說程式碼由下而上需經歷從object space轉換成world space再轉到view space (camera space或Eye coordinates) 之後再經投影，rasterization

Projections Orthographic Projections Perspective Projections 以一個中空的立方體模型為例，相同相機觀察角度 在正交投影中，看不到中空內側的部份 但在透視投影中，距離越遠長度差距越小的透視觀點，便可觀察到中空內側表面的部份

Pinhole camera A pinhole camera is a simple camera without a lens and with a single small aperture – effectively a light-proof box with a small hole in one side. 電腦圖學通常以Pinhole camera(針孔成像原理)，呈現出3D場景、鏡頭和成像平面間的關係

Frustum void glFrustum( ); GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble nearVal, GLdouble farVal ); far near Frustum 平面截頭體 可視為由相機為頂點，far plane為底面的大金字塔，截去以near plane為底面的小金字塔 這個形狀描述了針孔成像透視頭影的視野範圍(view volume)

Perspective Projections // Reset coordinate system glMatrixMode(GL_PROJECTION); glLoadIdentity(); // Produce the perspective projection gluPerspective(45.0f, fAspect, 1.0, 400.0); void gluPerspective( GLdouble fovy, GLdouble aspect, GLdouble zNear, GLdouble zFar); Frustum的參數設定較不直覺 gluPerspective提供了更方便的方式，讓開發者使用，內部再轉成Frustum的參數 Fovy 視角的大小，一般會設在30~60度之間 Aspect 長寬的比例，可根據視窗或viewport的長寬比例調整

攝影機使用與設定 Main Camera: 遊戲預設視角 點擊場景中的攝影機，可顯示預覽畫面

攝影機使用與設定 攝影機屬性 Background: 背景顏色 Projection:投影方式 Field of View(FOV) Perspective: 透視投影 Orthographic: 正交投影 Field of View(FOV) 可見視角範圍 Clipping Planes 最近(Near)與最遠(Far)能看到的範圍

Viewport transformation Modelview space Clipping space Viewport transformation Viewport 定義了Clipping space到視窗位置的轉換關係 一般而言，若只有一個viewport，會將viewport設定與視窗一樣大小，並根據viewport的長寬比例，調整投影的apsect ( gluPerspective()裡的長寬比例 ) 另外，一個視窗，可以由多個viewport對視窗進行分割顯示，每個viewport再對應到一個world space windows space

graphical perspective

First-Person perspective A graphical perspective rendered from the viewpoint of the player character http://www.youtube.com/watch?v=2N1TJP1cxmo Mirror's Edge https://www.youtube.com/watch?v=n5lu4Gyb1KM superhot doom Mirror's Edge

Second-person perspective In second person point of view, the action is shot from the perspective of a character that is not the protagonist. Let players feel as if they are actually the character they are controlling http://www.youtube.com/watch?v=82TSWzOsPYc mario 64 Mario 64

Third-person shooter The player character is seen at a distance from a number of different possible perspective angles. the player character is visible on-screen, and the gameplay consists primarily of shooting. http://www.youtube.com/watch?v=82TSWzOsPYc mario 64 https://www.youtube.com/watch?v=kFmYbaAjrfo Gear of war 3

Top-down perspective From God view Star craft 2 simcity https://www.youtube.com/watch?v=TqUCmlbkkS0 Star craft 2 simcity

Animation Squash & stretch The Prinicples of Animation, Squash and Stretch For hw2 Squash & stretch

Cameras and Actors

CameraFollow public GameObject player; private Vector3 offset; void start() { offset = transform.position –player.transform.position; } void LateUpdate() { transform.position = player.transform.position + offset; https://unity3d.com/learn/tutorials/projects/survival-shooter/camera-setup?playlist=17144

Vector3.Lerp public static Vector3 Lerp(Vector3 a, Vector3 b, float t); 𝑜𝑢𝑡= 1−𝑡 ∗𝑎+𝑡∗𝑏 https://docs.unity3d.com/ScriptReference/Vector3.Lerp.html

CameraFollow2 public GameObject player; public float smooth; private Vector3 offset; void start() { offset = transform.position –player.transform.position; } void LateUpdate() { Vector3 targetPos = player.transform.position + offset; transform.position = Vector3.Lerp (transform.position, targetPos, smooth*Time.deltaTime);

Lookat public void LookAt(Vector3 worldPosition); public void LookAt(Vector3 worldPosition, Vector3 worldUp = Vector3.up); +x +y +z up from void Update() { // Point the object at the world origin transform.LookAt(Vector3.zero); } https://docs.unity3d.com/ScriptReference/Transform.LookAt.html

An Actor Frame vForward Z vUp Y vLocation vRight X

Move object Translate public void Translate(Vector3 translation, Space relativeTo = Space.Self); public void Translate(float x, float y, float z, Space relativeTo = Space.Self); vForward Z vUp Y vLocation vRight X 對於3D空間的物件和相機，我們可以透過Frame座標系統描述他在空間中的位置和方向 也就是空間座標(x, y, z)和三軸的向量(前方、上方和側邊)， 這頁提供了一個GLFrame的C++ class，完整的實作可參見實習課的程式範例 由於三個軸是正交垂直，因此在class設計可只設定up和forward兩向量，用外積計算側邊向量 也可以透過這個物件本身座標系統來移動物體，沿著forward vector前進，是比較直覺的作法， 特別在遊戲中，上下左右的移動輸入，應該對應於物體本身的方向，而非對應世界座標軸的方向

Euler Angles vUp Y vForward Z vRight public void Rotate(Vector3 eulers, Space relativeTo = Space.Self); public void Rotate(float xAngle, float yAngle, float zAngle, Space relativeTo = Space.Self); vRight X 另外，物體的旋轉可以Euler Angles定義，就如同飛機飛行移動的三個旋轉方向 藉由Frame的定義對三軸做旋轉