computergraphics/Transform.cpp at master · katastreet/computergraphics · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
#include "Transform.h"

void RotateX(Vec3& Point,float theta){
    Matrix T(4,4); //Transformation matrix
    Matrix P(4,1); //Point matrix
    float angle = theta/180*pi;
    //Transformation matrix
    T(0,0) = 1;     T(0,1) = 0;         T(0,2) = 0;             T(0,3) = 0;
    T(1,0) = 0;     T(1,1) = cos(angle);T(1,2) = -sin(angle);   T(1,3) = 0;
    T(2,0) = 0;     T(2,1) = sin(angle);T(2,2) = cos(angle);    T(2,3) = 0;
    T(3,0) = 0;     T(3,1) = 0;         T(3,2) = 0;             T(3,3) = 1;
    //Point in matrix form
    P(0,0) = Point.x; P(0,1) = Point.y; P(0,2) = Point.z; P(0,3) = 1;

    P = T*P;
    Point.x = P(0,0);
    Point.y = P(0,1);
    Point.z = P(0,2);

}

void RotateY(Vec3& Point,float theta){
    Matrix T(4,4); //Transformation matrix
    Matrix P(4,1); //Point matrix
    float angle = theta/180*pi;
    //Transformation matrix
    T(0,0) = cos(angle);    T(0,1) = 0;         T(0,2) = sin(angle);    T(0,3) = 0;
    T(1,0) = 0;             T(1,1) = 1;         T(1,2) = 0;             T(1,3) = 0;
    T(2,0) = -sin(angle);   T(2,1) = 0;         T(2,2) = cos(angle);    T(2,3) = 0;
    T(3,0) = 0;             T(3,1) = 0;         T(3,2) = 0;             T(3,3) = 1;
    //Point in matrix form
    P(0,0) = Point.x; P(0,1) = Point.y; P(0,2) = Point.z; P(0,3) = 1;

    P = T*P;
    Point.x = P(0,0);
    Point.y = P(0,1);
    Point.z = P(0,2);

}


void RotateZ(Vec3& Point,float theta){
    Matrix T(4,4); //Transformation matrix
    Matrix P(4,1); //Point matrix
    float angle = theta/180*pi;
    //Transformation matrix
    T(0,0) = cos(angle);    T(0,1) = -sin(theta);       T(0,2) = 0;    T(0,3) = 0;
    T(1,0) = sin(angle);    T(1,1) = cos(theta);        T(1,2) = 0;    T(1,3) = 0;
    T(2,0) = 0;             T(2,1) = 0;                 T(2,2) = 1;    T(2,3) = 0;
    T(3,0) = 0;             T(3,1) = 0;                 T(3,2) = 0;    T(3,3) = 1;
    //Point in matrix form
    P(0,0) = Point.x; P(0,1) = Point.y; P(0,2) = Point.z; P(0,3) = 1;

    P = T*P;
    Point.x = P(0,0);
    Point.y = P(0,1);
    Point.z = P(0,2);

}

void Translate(Vec3& Point,const Vec3& tMat){
    Matrix T(4,4); //Transformation matrix
    Matrix P(4,1); //Point matrix
    //Transformation matrix
    T(0,0) = 1;    T(0,1) = 0;      T(0,2) = 0;    T(0,3) = tMat.x;
    T(1,0) = 0;    T(1,1) = 1;      T(1,2) = 0;    T(1,3) = tMat.y;
    T(2,0) = 0;    T(2,1) = 0;      T(2,2) = 1;    T(2,3) = tMat.z;
    T(3,0) = 0;    T(3,1) = 0;      T(3,2) = 0;    T(3,3) = 1;
    //Point in matrix form
    P(0,0) = Point.x; P(0,1) = Point.y; P(0,2) = Point.z; P(0,3) = 1;

    P = T*P;
    Point.x = P(0,0);
    Point.y = P(0,1);
    Point.z = P(0,2);

}

Vec2 World_To_Pixel(const Vec3& source ,const Vec3& camera, const Vec3& LookTo,float planeWidth, float planeHeight, float winWidth, float winHeight){
    //first determine the World to Camera transforming matrix
    Matrix WtoC(4,4);
    //for that use the concept of N, U and V unit vectors
    Vec3 N,U,V(0,1,0);

    //calculate the N unit vector
    //N is the vector from LookTo point to Camera point
    N = camera-LookTo;
    N = N/ N.magnitude();

    //U = V X N
    U = V.crossProduct(N);
    U = U / U.magnitude();


    //readjust the V vector
    V = N.crossProduct(U);
    V = V / V.magnitude();
//
//    std::cout << U.x << " "<< U.y << " "<< U.z << std::endl;
//    std::cout << V.x << " "<< V.y << " "<< V.z << std::endl;
//    std::cout << N.x << " "<< N.y << " "<< N.z << std::endl;
//    std::cout << std::endl <<std::endl ;

    //Transpose matrix from World co-ordinate to View co-ordinate
    Matrix T(4,4);
    T(0,0) = 1 ; T(0,1) = 0; T(0,2) = 0; T(0,3) = -camera.x;
    T(1,0) = 0 ; T(1,1) = 1; T(1,2) = 0; T(1,3) = -camera.y;
    T(2,0) = 0 ; T(2,1) = 0; T(2,2) = 1; T(2,3) = -camera.z;
    T(3,0) = 0 ; T(3,1) = 0; T(3,2) = 0; T(3,3) = 1;

    //Rotation Matrix
    Matrix R(4,4);
    R(0,0) = U[0] ; R(0,1) = U[1]; R(0,2) = U[2]; R(0,3) = 0;
    R(1,0) = V[0] ; R(1,1) = V[1]; R(1,2) = V[2]; R(1,3) = 0;
    R(2,0) = N[0] ; R(2,1) = N[1]; R(2,2) = N[2]; R(2,3) = 0;
    R(3,0) = 0 ; R(3,1) = 0; R(3,2) = 0; R(3,3) = 1;


    //Calculating the WtoC matrix W = T*R (rotate and then translate)
    WtoC = R*T;
//
//    std::cout << std::endl << " MATRIX START" << std::endl;
//    WtoC.print();
//    std::cout <<"MATRIX END"<< std::endl << std::endl;

    Matrix S(4,1); //The source point in matrix form
    S(0) = source.x ; S(1) = source.y; S(2) = source.z ; S(3) = 1;

    S = WtoC * S;
//    //S now represents the camera co-ordinate system's values
//    std::cout << S(0) << " " << S(1) << " "<<S(2) <<std::endl;
//    //calculate the screen pixels


    Vec2 retVal;
    retVal.x = S(0) / -S(2);
    retVal.y = S(1) / -S(2);

    //normalize the screen pixels
    retVal.x = (retVal.x + planeWidth*0.5)/planeWidth;
    retVal.y = (retVal.y + planeHeight*0.5)/planeHeight;

    //now to original screen pos in computer
    retVal.x = (int)(retVal.x * winWidth);
    retVal.y = (int)((1-retVal.y) * winHeight);

    retVal.z = S(2);

    return retVal;
}