Vector Algebra - Hallymgraphics.hallym.ac.kr/teach/2007/gp1/src/02prac.pdf · 2008. 9. 16. · Game...

Game Programming I

Sun-Jeong Kim http://www.hallym.ac.kr/~sunkim/teach/2007/gp1

Vector Algebra

2nd Week, 2007


Downloading DirectX 9.0 SDK


Sample Programs (1)


Sample Programs (2)

“Book2Part1Code.zip”


Microsoft Visual Studio .Net


File New Project…

Visual C++ Win32Win32 Consol Project


Application Settings

Empty project


‘Chap01’ Solution


Adding the Source Code (1)

Copying the source code



Project Add Existing Item




Linking the Library Files

Project PropertiesConfiguration Properties Linker Input

Additional Dependencies : d3dx9.lib


Result


D3DXVECTOR3 Class


Useful Functions

Computing the length of a vector

Normalizing a vector

Computing the dot product of two vectors

Computing the cross product of two vectors


D3DXVec3 – “main.cpp” (1)#include <d3dx9.h>#include <iostream>using namespace std;

// Overload the "<<" operators so that we can use cout to // output D3DXVECTOR3 objects.

ostream& operator<<(ostream& os, D3DXVECTOR3& v){

os << "(" << v.x << ", " << v.y << ", " << v.z << ")";return os;

}

int main(){

// Using constructor, D3DXVECTOR3(FLOAT x, FLOAT y, FLOAT z);D3DXVECTOR3 u(1.0f, 2.0f, 3.0f);

// Using constructor, D3DXVECTOR3(CONST FLOAT *);float x[3] = {-2.0f, 1.0f, -3.0f};D3DXVECTOR3 v(x);

// Using constructor, D3DXVECTOR3() {};D3DXVECTOR3 a, b, c, d, e;

// Vector addition: D3DXVECTOR3 operator + a = u + v;


D3DXVec3 – “main.cpp” (2)// Vector subtraction: D3DXVECTOR3 operator -b = u - v;

// Scalar multiplication: D3DXVECTOR3 operator * c = u * 10;

// ||u||float length = D3DXVec3Length(&u);

// d = u / ||u||D3DXVec3Normalize(&d, &u);

// s = u dot vfloat s = D3DXVec3Dot(&u, &v);

// e = u x vD3DXVec3Cross(&e, &u, &v);

cout << "u = " << u << endl;cout << "v = " << v << endl;cout << "a = " << a << endl;cout << "b = " << b << endl;cout << "c = " << c << endl;cout << "d = " << d << endl;cout << "e = " << e << endl;cout << "||u|| = " << length << endl;cout << "u dot v = " << s << endl;

return 0;}


Example 1.4

Let and . Find the angle between and .

( )3,2,1=ur ( )1,0,4 −−=v

r

ur

vr

θcosvuvurrrr

=⋅

( ) ( )( ) ( )

1714

7

104321

130241

cos

222222

222222

−=

−++−++

−⋅+⋅+−⋅=

++++

++=

⋅=

zyxzyx

zzyyxx

vvvuuu

vuvuvu

vu

vurr

rr

θ

°≈⎟⎠

⎞⎜⎝

⎛ −=∴ − 117

1714

7cos 1θ


Example 1.4 – Program


Example 1.4 – Result


Example 1.6

Let and . Compute and , and verify that is orthogonal to and that is orthogonal to .

( )3,1,2=ur ( )0,0,2=v

rvuwrrr

×=wr

ur

vr

( ) ( ) ( )( )zyyxzxxzyzzy vuvuvuvuvuvuvu −−−=× ,,rr

( ) ( ) ( )( )( )2,6,0

2102,0223,0301

−=⋅−⋅⋅−⋅⋅−⋅=w

r

( ) 0321620 =⋅−+⋅+⋅=⋅uwrr

( ) 0020620 =⋅−+⋅+⋅=⋅vwrr

uvyrrr

×=wr

( ) ( ) ( )( )( )2,6,0

2012,3220,1030

−=⋅−⋅⋅−⋅⋅−⋅=y

r

∴ is orthogonal to and .wr

ur

vr


Example 1.6 – Program


Example 1.6 – Result


Exercise

Program the following questions:

(Exercise 4) Is the angle between and orthogonal, acute, or obtuse?

(Exercise 10) Let the following points define a triangle relative to some coordinate system: A=(0,0,0), B=(0,1,3), and C=(5,1,0). Find a vector orthogonal to this triangle. (Hint: Find two vectors on two of the triangle’s edges and use the cross product.)

ur

vr

( ) ( )2,2,2 ,1,1,1 == vurr

( ) ( )0,2,2 ,0,1,1 −== vurr

( ) ( )0,1,3 ,1,1,1 =−−−= vurr


연습 문제 (1)

다음질문의프로그램을작성하여답하시오.

(Exercise 4) 다음각각의두벡터 와 가이루는각이직각인가예각인가둔각인가?

(Exercise 10) 어떤좌표계에서세점 A=(0,0,0), B=(0,1,3), C=(5,1,0)가한삼각형을정의한다고하자. 이삼각형에수직인벡터를구하시오. (힌트: 삼각형모서리에있는두개의벡터를구한다음, 외적을이용한다.)

ur

vr

( ) ( )2,2,2 ,1,1,1 == vurr

( ) ( )0,2,2 ,0,1,1 −== vurr

( ) ( )0,1,3 ,1,1,1 =−−−= vurr


연습 문제 (2)

제출방법2007. 3. 15수업시간전까지

Exercise 4와 10에대한프로그램각각을작성 (예: “ex04.cpp”와 “ex10.cpp”) + 실행결과 (본강의자료20쪽또는 23쪽과같은출력이미지, 예: “ex04.jpg”와“ex10.jpg”)

4개파일을압축한 “학번.zip”을웹에 upload 할것

Vector Algebra - Hallymgraphics.hallym.ac.kr/teach/2007/gp1/src/02prac.pdf · 2008. 9. 16. · Game...

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Transcript of Vector Algebra - Hallymgraphics.hallym.ac.kr/teach/2007/gp1/src/02prac.pdf · 2008. 9. 16. · Game...