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w15

1.根據 roc_list_coord_flag.7z 程式內容所印出的六組 ABED 等繪製 ROC 國旗白日圖案中的菱形四個關鍵點, 請直接在青天與滿地紅的圖案中, 利用白色作為畫線顏色, 將第二組的 ABED 等四個點的座標, 以直線相連.。

#include <stdio.h>
#include <gd.h>
#include <math.h>

void draw_roc_flag(gdImagePtr img);

int main() {
    // width 3: height 2
    int width = 1200;
    // 國旗長寬比為 3:2
    int height = (int)(width * 2.0 / 3.0);

    gdImagePtr img = gdImageCreateTrueColor(width, height);
    gdImageAlphaBlending(img, 0);

    draw_roc_flag(img);

    FILE *outputFile = fopen("roc_flag_in_gd.png", "wb");
    if (outputFile == NULL) {
        fprintf(stderr, "Error opening the output file.\n");
        return 1;
    }
    gdImagePngEx(img, outputFile, 9);
    fclose(outputFile);
    gdImageDestroy(img);
    return 0;
}

void draw_roc_flag(gdImagePtr img) {
    int width = gdImageSX(img);
    int height = gdImageSY(img);
    int red, white, blue;
    // 白日位於青天面積正中央, 因此中心點座標為長寬各 1/4 處
    int center_x = (int)(width / 4);
    int center_y = (int)(height / 4);
    // gdImageFilledEllipse 需以長寬方向的 diameter 作圖
    // 由於中央白日圓形的半徑為青天寬度的 1/8
    // 因此中央白日圓形的直徑為青天寬度的 1/4, 也就是國旗寬度的 1/8
    // 而且白日十二道光芒的外圍圓形其半徑也是國旗寬度的1/8
    int sun_radius = (int)(width / 8);
    // 中央白日圓形的直徑等於十二道光芒外圍圓形的半徑
    int white_circle_dia = sun_radius;
    // 中央藍色圓形半徑為中央白日的 1又 2/15
    int blue_circle_dia = white_circle_dia + white_circle_dia * 2 / 15;
    // 根據 https://www.moi.gov.tw/cp.aspx?n=10621 訂定國旗三種顏色值
    red = gdImageColorAllocate(img, 255, 0, 0);    // 紅色
    white = gdImageColorAllocate(img, 255, 255, 255); // 白色
    blue = gdImageColorAllocate(img, 0, 0, 149);    // 藍色
    // 根據畫布大小塗上紅色長方形區域
    gdImageFilledRectangle(img, 0, 0, width, height, red);
    // 青天面積為整面國旗的 1/4, 也是採用長方形塗色
    gdImageFilledRectangle(img, 0, 0, (int)(width / 2.0), (int)(height / 2.0), blue);
    // 利用一個藍色大圓與白色小圓畫出藍色環狀
    gdImageFilledEllipse(img, center_x, center_y, blue_circle_dia, blue_circle_dia, blue);
    gdImageFilledEllipse(img, center_x, center_y, white_circle_dia, white_circle_dia, white);

    // 連接四個點
    int points[8];
    points[0] = 429;
    points[1] = 125;
    points[2] = 279;
    points[3] = 165;
    points[4] = 170;
    points[5] = 274;
    points[6] = 170;
    points[7] = 274;

    // 使用白色線條連接四個點
    gdImageLine(img, points[0], points[1], points[2], points[3], white);
    gdImageLine(img, points[2], points[3], points[4], points[5], white);
    gdImageLine(img, points[4], points[5], points[6], points[7], white);
    gdImageLine(img, points[6], points[7], points[0], points[1], white);
}

2.承上題, 請列出第二組 ABED 的四條直線與白日中的大圓所相交 (intersect) 的四個點座標.

#include <stdio.h>
#include <gd.h>
#include <math.h>

void draw_roc_flag(gdImagePtr img);
int findIntersection(gdImagePtr img, int x1, int y1, int x2, int y2, int cx, int cy, int r, int *inter_x, int *inter_y);

int main() {
    // width 3: height 2
    int width = 1200;
    // 國旗長寬比為 3:2
    int height = (int)(width * 2.0 / 3.0);

    gdImagePtr img = gdImageCreateTrueColor(width, height);
    gdImageAlphaBlending(img, 0);

    draw_roc_flag(img);

    FILE *outputFile = fopen("roc_flag_in_gd.png", "wb");
    if (outputFile == NULL) {
        fprintf(stderr, "Error opening the output file.\n");
        return 1;
    }
    gdImagePngEx(img, outputFile, 9);
    fclose(outputFile);
    gdImageDestroy(img);

    return 0;
}

void draw_roc_flag(gdImagePtr img) {
    int width = gdImageSX(img);
    int height = gdImageSY(img);
    int red, white, blue;
    // ... (同樣的畫圖程式碼)

    // 連接四個點
    int points[8];
    points[0] = 429;
    points[1] = 125;
    points[2] = 279;
    points[3] = 165;
    points[4] = 170;
    points[5] = 274;
    points[6] = 170;
    points[7] = 274;

    // 使用白色線條連接四個點
    gdImageLine(img, points[0], points[1], points[2], points[3], white);
    gdImageLine(img, points[2], points[3], points[4], points[5], white);
    gdImageLine(img, points[4], points[5], points[6], points[7], white);
    gdImageLine(img, points[6], points[7], points[0], points[1], white);

    // 找出白線與圓形相交的點
    int inter_x, inter_y;
    findIntersection(img, points[0], points[1], points[2], points[3], width / 4, height / 4, width / 8, &inter_x, &inter_y);
    printf("Intersection Point 1: (%d, %d)\n", inter_x, inter_y);

    findIntersection(img, points[2], points[3], points[4], points[5], width / 4, height / 4, width / 8, &inter_x, &inter_y);
    printf("Intersection Point 2: (%d, %d)\n", inter_x, inter_y);

    findIntersection(img, points[4], points[5], points[6], points[7], width / 4, height / 4, width / 8, &inter_x, &inter_y);
    printf("Intersection Point 3: (%d, %d)\n", inter_x, inter_y);

    findIntersection(img, points[6], points[7], points[0], points[1], width / 4, height / 4, width / 8, &inter_x, &inter_y);
    printf("Intersection Point 4: (%d, %d)\n", inter_x, inter_y);
}

int findIntersection(gdImagePtr img, int x1, int y1, int x2, int y2, int cx, int cy, int r, int *inter_x, int *inter_y) {
    // 將直線轉換成一般形式 Ax + By = C
    double A = y2 - y1;
    double B = x1 - x2;
    double C = A * x1 + B * y1;

    // 計算圓心到直線的距離
    double distance = fabs(A * cx + B * cy - C) / sqrt(A * A + B * B);

    // 如果距離小於半徑，表示相交
    if (distance <= r) {
        // 計算交點座標
        double d = A * A + B * B;
        *inter_x = (int)((B * (B * cx - A * cy) - A * C) / d);
        *inter_y = (int)((A * (-B * cx + A * cy) - B * C) / d);

        // 補償畫布的偏移
        *inter_x += gdImageSX(img) / 2;
        *inter_y += gdImageSY(img) / 2;

        return 1;  // 表示有相交點
    }

    return 0;  // 表示沒有相交點
}


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