基础知识

Vertex（顶点）

define the location of primitives in space, and consists of vertex stream.

顶点用于定义空间中基本图形（primitives）的位置。它包含了一个顶点流（vertex stream），通常这个顶点流包含了多个顶点。每个顶点包括了定义其在三维空间中位置的坐标信息，以及可能包括颜色、纹理坐标和法线等其他属性。

Primitive

1. the result of the interpretation of a vertex stream, as part of Primitive Assembly 作为图元装配（Primitive Assembly）的一部分，图元是顶点流解释的结果。简单地说，图元是由顶点通过特定的规则连接起来形成的基本图形，如点、线和三角形。

2. the interpretation scheme used by opengl to determine what a stream of vertices represents when being rendered. 在OpenGL中，图元也指定了如何解释顶点流来渲染。OpenGL根据定义的图元类型（例如点、线段、三角形）来决定如何将一连串的顶点组合成图形。

Fragment

a fragment is a collection of values produced by the Rasterization. Each fragment represents a sample-sized segment of a rasterized primitive. 片元是光栅化（Rasterization）过程产生的值的集合。每个片元代表了光栅化图元的一个样本大小的部分。 片元包含了用于最终像素颜色计算的所有数据，比如颜色、深度以及其他可能的属性。在图形管线中，片元着色器（Fragment Shader）会处理这些片元，以生成最终在屏幕上显示的像素颜色。

Graphics Pipeline

There are three stages

• Application Stage

• Geometry Stage

• Rasterization Stage

Viewing process 视图处理过程

• Transform into camera coordinates.

• Perform projection into view volume.

• Clip geometry outside the view volume.

• Perform Perspective-division into NDC.

• Remove hidden surfaces

Local space -> world space -> camera space -> clipping space -> NDC -> viewport

1 Zooming

Adjusting the viewport can implement zooming 调整视口大小和位置可以实现缩放功能。缩放时，你实际上是改变了最终图像在屏幕上显示的尺寸。

Adjusting the clipping window can implement broadening or shrinking what we see 调整裁剪窗口（即在裁剪空间中决定哪些部分是可见的）可以实现对可见场景的扩大或缩小，从而改变用户看到的场景范围。

2 View Volume

术语“view volume”（视图体积）和“clipping volume”（裁剪体积）通常可以视为相同的概念，在某些情况下可以互换使用。

2.1 Orthographic view volume

• Preserves both distances and angles

• Shapes preserved

• Can be used for measurements

  • Building plans

  • Manuals

• Cannot see what object really looks like because many surfaces are hidden from view

• Often we add isometric

2.2 Perspective view volume

• Objects further from viewer are projected smaller than the same sized objects closer to the viewer (diminution) • Looks realistic

• Equal distances along a line are not projected into equal distances (nonuniform foreshortening)

• Angles preserved only in planes parallel to the projection plane

• More difficult to construct by hand than parallel projections (but not more difficult by computer)

3 Normalized Device coordinates (NDC)

4 Geometry vs Topology

geometry: locations of the vertices

topology: organization of the vertices and edges

Topology holds even if geometry changes.

Solid modeling

Surfaced based & volume based

1 Surface based

1.1 Mesh Based 边界表示（Boundary Representation, B-rep）

The size and shape is defined by the faces, edges and vertices which consists of its boundary.

(low-dimensional elements)

• Pros: flexible and computers can render them quickly. The vast majority of 3D models today are built as textured polygonal models

• Cons: polygons are planar and need approximate curved surfaces using many polygons, representation is not unique

很难闭合

1.2 Constructive solid geometry(CSG) 构造实体几何

A solid is defined as the result of a sequence of regularized Boolean operations.

• Pros: Computer-Aided Manufacturing: a brick with a hole drilled through it is represented as “just

that” and CSG can easily assure that objects are “solid” or water-tight

• Cons: Relationships between objects might be very complex (search the entire tree) Real world objects may get very complex

2 Volume based

Spatial decomposition: voxel octree BSP 体素（voxels）、八叉树（octree）和二叉空间分割（Binary Space Partitioning, BSP）等技术

2.1 Voxels: a volume element

Pros:

• Modelling continues phenomena: medicine, geology, body, etc.

• Regular data

• Easy to compute volume, make slices

Cons:

• Massive data for high resolution

• The surface is always somehow “rough”

3 Point based

3.1 Point cloud

• Easily accessed with laser scanning, range camera or

stereo image matching

• No connectivity

• Widely used!

GLSL

1 Vertex shader

• Transform vertices

• Model, View and projection transformations

• Custom transformation

  • Morphing

  • Wave motion

• Lighting

• Color

• Normal

• Other per-vertex properties

顶点着色器可以执行多种任务，比如变换顶点的位置、处理顶点的颜色和纹理坐标、计算光照等。

通常，它会将顶点从一个坐标系统转换到另一个坐标系统，例如从模型坐标转换到视图坐标。

2 Fragment shader

• Compute the color of a fragment/pixel

• The input data is from rasterization and textures and other values

确定每个片元的最终颜色和其他属性。这个过程可能包括纹理映射、光照和阴影计算、颜色混合等。

3 VAO VBO EBO

1. VAO（顶点数组对象，Vertex Array Object）:

   1. VAO是一个对象，它存储了所有的顶点属性状态（如顶点属性的布局）和与这些属性相关的VBO。

   2. 使用VAO的目的是为了保存顶点属性的配置和数据源。当配置顶点属性指针时，这些配置会存储在当前绑定的VAO中。

   3. 在渲染时，只需绑定相应的VAO，就可以使用其中的顶点属性配置和数据。

2. VBO（顶点缓冲对象，Vertex Buffer Object）:

   1. VBO用于在GPU内存中存储大量顶点的数据，如顶点坐标、纹理坐标、法线、颜色等。

   2. VBO的使用可以大幅减少CPU到GPU的通信，提高渲染效率，因为顶点数据可以在渲染之前发送到GPU，然后在渲染时直接从GPU内存中获取。

   3. 在使用VBO时，顶点数据只需上传一次到GPU，之后可以多次用于渲染，这对于动画和复杂场景渲染非常有效。

3. EBO（元素缓冲对象，Element Buffer Object）:

   1. EBO也称为索引缓冲对象（Index Buffer Object），用于存储顶点索引。

   2. 使用EBO可以重用顶点数据，定义哪些顶点会组成一个图元（如三角形）。这样，相同的顶点可以被多次引用，减少了内存的使用和数据传输。

   3. EBO通常与VBO一起使用，VBO存储顶点数据，EBO存储构成图元的顶点索引。