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We give the special names row vector and column vector to describe such matrices. Examples of a row and column vector follow: v = [v1, v 2 , v3 , v 4 ] éu x ù u = êêu y úú êëu z úû When using row or column vectors, we only need a single subscript, and sometimes we use letters as the subscripts used to identify an entry in the row or column. Equality, Scalar Multiplication, and Addition Refer to the following four matrices throughout this subsection: é 1 5ù A=ê ú ë- 2 3û n n é6 2 ù B=ê ú ë5 - 8 û é 1 5ù C=ê ú ë- 2 3û é 1 2 -1 3 ù D=ê ú ë- 6 3 0 0 û Two matrices are equal if they are of the same dimension and their corresponding entries are equal.

CONST D3DXPLANE *pP // Input plane. ); Transforming a Plane Lengyel shows in Mathematics for 3D Game Programming & Computer $ d) by treating it as a 4D vecGraphics that we can transform a plane (n, tor and multiplying it by the inverse-transpose of the desired transformation matrix. Note that the plane’s normal vector must be normalized first. We use the following D3DX function to do this: D3DXPLANE *D3DXPlaneTransform( D3DXPLANE *pOut, // Result CONST D3DXPLANE *pP, // Input plane. CONST D3DXMATRIX *pM // Transformation matrix.

The second theme is to learn the steps necessary to take a 2D “picture” of the 3D world based on what the camera “sees”; these steps as a whole are referred to as the rendering pipeline. Chapter 3, “Drawing in Direct3D”—This chapter shows how to draw 3D geometry in Direct3D. We learn how to store geometric data in a form that is usable by Direct3D, and we learn the Direct3D drawing commands. In addition, we learn how to configure the way that Direct3D draws geometry using render states. Chapter 4, “Color”—In this chapter, we learn how color is represented in Direct3D and how to apply color to solid 3D geometric primitives.

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