We use vectors to represent positions, displacements, directions, velocities, and forces, for example. In this chapter, we study vectors and the operations used to manipulate them. Chapter 2 Matrix Algebra: Matrices provide an efficient and compact way of representing transformations. In this chapter, we become familiar with matrices and the operations defined on them.

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We use vectors to represent positions, displacements, directions, velocities, and forces, for example. In this chapter, we study vectors and the operations used to manipulate them. Chapter 2 Matrix Algebra: Matrices provide an efficient and compact way of representing transformations. In this chapter, we become familiar with matrices and the operations defined on them. Chapter 3 Transformations; Planes: This chapter examines three fundamental geometric transformations: scaling, rotation, and translation.

We use these transformations to manipulate 3D objects in space. In addition, a brief primer on 3D planes is provided; planes are useful for dividing and sorting 3D space. Chapter 4 Direct3D Initialization: In this chapter, we learn what Direct3D is about and how to initialize it in preparation for 3D drawing. Basic Direct3D topics are also introduced, such as surfaces, pixel formats, double buffering, and multisampling.

In addition, we show how to output 2D text, and give some tips on debugging Direct3D applications. We learn how to measure time with the performance counter, which we use to compute the frames rendered per second. In addition, we learn how to initialize and use Direct Input for keyboard and mouse input.

Finally, we give an introduction to 2D graphics programming with the ID3DXSprite interface to give a flavor for graphics programming. Chapter 6 The Rendering Pipeline: The first theme of this chapter is to learn, mathematically, how to describe a 3D world and represent a virtual camera that describes the volume of space the camera "sees.

We learn how to store geometric data in a form usable by Direct3D, and we learn the Direct3D drawing commands. In addition, we also write our first simple vertex and pixel shaders using the HLSL high level shading language and effects framework i. We also show how to configure the way in which Direct3D draws geometry using render states. We conclude by examining the D3DX functions used to create simple geometric meshes like cylinders, spheres, boxes, and teapots.

Chapter 8 Color: In this chapter, we learn how color is represented in Direct3D and how to apply color to solid 3D geometric primitives. We also show how we can animate the position and color of vertices completely in a vertex shader with the colored wave demo. Finally, we describe two render states that control how colors, specified per vertex, can be shaded across a primitive. Chapter 9 Lighting: In this chapter, we learn how to create light sources and define the interaction between light and surfaces.

In particular, we show how to implement directional lights, point lights, and spotlights with vertex and pixel shaders, which mimic the traditional lighting fixed function pipeline lighting model. We also show how to do per pixel lighting with interpolated per pixel normal vectors i. Chapter 10 Texturing: This chapter describes texture mapping, which is a technique used to increase the realism of the scene by mapping 2D image data onto a 3D primitive.

For example, using texture mapping, we can model a brick wall by applying a 2D brick wall image onto a 3D rectangle. Other key texturing topics covered include multi-texturing, and animated texture transformations.

As always, all of our work is done in the programmable pipeline with vertex and pixel shaders. Chapter 11 Blending: In this chapter, we look at a technique called blending, which allows us to implement a number of special effects like transparency. In addition, we discuss the alpha test, which enables us to mask out certain parts of an image from showing up; this can be used to implement gates, for example.

An exercise gets you started on implementing y-axis aligned billboards, which, when combined with the alpha test, enable us to simulate trees. Chapter 12 Stenciling: This chapter describes the stencil buffer, which, like a stencil, allows us to block pixels from being drawn.

To illustrate the ideas of this chapter, we include a thorough discussion on implementing reflections and planar shadows using the stencil buffer. An exercise describes an algorithm for using the stencil buffer to render the depth complexity of a scene, and asks you to implement the algorithm. Chapter 13 Meshes: This chapter shows how to work with. In addition, many of the D3DX mesh functions are surveyed. We also show how to compute the bounding box and sphere of a mesh.

Chapter 14 Mesh Hierarchy Animation Part I: In this chapter, we learn the relationship between a child mesh and its parent mesh, and how to model this hierarchy relationship in code.

To demonstrate the ideas, we create and animate some simple mesh hierarchies, namely a robot arm and solar system. Chapter 15 Mesh Hierarchy Animation Part II: With the theory of mesh hierarchies covered in the previous chapter, we focus now on implementing the vertex blending algorithm to model elastic skin. We demonstrate this technique by loading the animation and skinning data from a.

X file, and then animating it with vertex blending. We use the D3DX animation interfaces. Chapter 16 Terrain Rendering Part I: This chapter shows how to create, texture, light, and render 3D terrains using heightmaps and a multi-texturing technique. Furthermore, we show how to smoothly "walk" the camera over the terrain.

We also learn how to divide the terrain mesh into sub-grid chunks in preparation for frustum culling. In addition, we embellish our terrain scene by adding trees, a castle, fog, and animated grass. Chapter 18 Particle Systems: In this chapter, we learn how to model systems that consist of many small particles that all behave in a similar manner.

For example, particle systems can be used to model falling snow and rain, fire and smoke, rocket trails and particle guns, and sprinklers and fountains. Chapter 19 Picking: This chapter shows how to determine the particular 3D object or 3D primitive that the user has selected with the mouse.

Picking is often a necessity in 3D games and applications where the user interacts with the 3D world with the mouse. Chapter 20, Advanced Texturing Part I: In this chapter, we show how to reflect environments onto arbitrary meshes with environment mapping; in addition, we use an environment map to texture a sky-sphere. We also show how to get detailed real-time lighting using normal maps, which can also be used to simulate water waves. In particular, we discuss projective texturing, shadow mapping, and displacement mapping.

Shadow mapping is a real-time shadowing technique, which shadows arbitrary geometry it is not limited to planar shadows. Finally, displacement mapping is a technique where each vertex has an associated displacement vector, which specifies how a vertex should be displaced in a vertex shader.

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