數媒筆記整理2

最近收拾資料，發現之前的數媒筆記只整理了一篇，這幾天陸續補上吧。

1. 題目：2D transformation, polygon clipping, viewport

1.1. Goal

You are to write a program that receive a series of commands, and display result on screen. The commands will tell you how build your 2D world, and how to display it on screen. Your program must read the commands from a file called hw2.in.

1.2. Commands

• square: create a square in your 2D world. 即畫一個正方形
• triangle: create a triangle in your 2D world. 即畫一個三角形
• translate X Y: do a translation by (X, Y), multiply the current matrix by a translation matrix
• scale X Y: do a scaling by (X, Y), multiply the current matrix by a scaling matrix
• rotate X Y: do a rotation by R degree, multiply the current matrix by a rotation matrix
• view WL WR WB WT VL VR VB VT: WL WR WB WT (world left, world right, world bottom, world top), these 4 values specify a rectangle clip area of your 2D world. VL VR VB VT (view left, view right, view bottom, view top), these 4 values specify a viewport area in screen space.
  

1.3. Examples

# create a square and its transformation
reset
scale 2.0 2.0
rotate 45.0
translate 10.0 10.0
square
# display the world in viewports
view 0.0 20.0 0.0 20.0 100 400 100 400
end

2. 分析：

實驗環境在：VS下搭配OpenGlut開發，畫點和畫線部分既可以用已經封裝好的庫函數，也可以用自己實現的畫線函數。這裏主要就是線性代數中的矩陣變換，根據題目要求，對矩陣實現相應的左右乘法運算。

3.源碼

void Translate(float a,  float b)  {
    int i,  j,  k;
    float translation_matrix[3][3];
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            temp_matrix[i][j] = current_transform_matrix[i][j];
            current_transform_matrix[i][j] = 0;
            translation_matrix[i][j] = 0;
        }
    }
    translation_matrix[0][2] = a;
    translation_matrix[1][2] = b;
    translation_matrix[0][0] = 1;
    translation_matrix[1][1] = 1;
    translation_matrix[2][2] = 1;
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            for (k = 0 ; k < 3 ; k++)  {
                current_transform_matrix[i][j] += translation_matrix[i][k] * temp_matrix[k][j];
            }
        }
    }
    cout << "After Translate, Current Transform matrix:" << endl;
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            cout << current_transform_matrix[i][j] << " ";
        }
        cout << endl;
    }
    cout << endl;
}


void Rotate(float a)  {
    float rotation_matrix[3][3];
    int i,  j,  k;
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            rotation_matrix[i][j] = 0;
            temp_matrix[i][j] = current_transform_matrix[i][j];
            current_transform_matrix[i][j] = 0;
        }
    }
    rotation_matrix[0][0] = cos((a / 180.0 * 3.14159265 ));
    rotation_matrix[0][1] = -sin((a / 180.0 * 3.14159265 ));
    rotation_matrix[1][0] = sin((a / 180.0 * 3.14159265 ));
    rotation_matrix[1][1] = cos((a / 180.0 * 3.14159265 ));
    rotation_matrix[2][2] = 1;
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            for (k = 0 ; k < 3 ; k++)  {
                current_transform_matrix[i][j] += rotation_matrix[i][k] * temp_matrix[k][j];
            }
        }
    }
    cout << "After Rotate, Current Transform matrix:" << endl;
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            cout << current_transform_matrix[i][j] << " ";
        }
        cout << endl;
    }
    cout << endl;
}


void Scale(float a,  float b)  {
    float scaling_matrix[3][3];
    int i,  j,  k;
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            scaling_matrix[i][j] = 0;
            temp_matrix[i][j] = current_transform_matrix[i][j];
            current_transform_matrix[i][j] = 0;
        }
    }
    scaling_matrix[0][0] = a;
    scaling_matrix[1][1] = b;
    scaling_matrix[2][2] = 1;
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            for (k = 0 ; k < 3 ; k++)  {
                current_transform_matrix[i][j] += scaling_matrix[i][k] * temp_matrix[k][j];
            }               
        }
    }
    cout << "After Scale, Current Transform matrix:" << endl;
    for (i = 0 ; i < 3 ; i++)  {
        for (j = 0 ; j < 3 ; j++)  {
            cout << current_transform_matrix[i][j] << " ";
        }
        cout << endl;
    }
    cout << endl;
}

4. 效果

全部源碼整理之後會掛在筆者的github倉庫裏面：https://github.com/liby3/ComputerGraphicProject
歡迎有興趣的童鞋一起學習。