World Space 与 canonical view volume 是两个不同的空间 World Space (起点) $\xrightarrow{\text{相机变换}}$ Camera Space $\xrightarrow{\text{投影变换}}$ Canonical View Volume (中转站) $\xrightarrow{\text{视口变换}}$ Screen Space
The Viewport Transformation
规范视体积” (canonical view volume) 中，并且我们希望用一个看向 $-z$ 方向的正交相机来观察它，规范视体积是一个包含所有笛卡尔坐标在 $-1$ 和 $+1$ 之间的 3D 点的立方体——即 $(x, y, z) \in [-1, 1]^3$ 典型视图体积是一个边长为二、以原点为中心的立方体。
construct M_vp // 构建视口变换矩阵 construct M_orth // 构建正交投影矩阵 M = M_vp * M_orth // 关键步骤：矩阵预合并！ for each line segment (a_i, b_i) do // 遍历每一条线 p = M * a_i // 用合并后的矩阵变换点 a q = M * b_i // 用合并后的矩阵变换点 b drawline(x_p, y_p, x_q, y_q) // 画线（只用 x, y 坐标）
相机变换 (The Camera Transformation)
我们希望能能够在 3D 空间中改变视点，并朝向任意方向观察。关于如何指定观察者的位置和朝向，存在许多不同的惯例。我们将采用如下定义 ：
construct M_vp // 构建视口矩阵 construct M_orth // 构建正交投影矩阵 construct M_cam // 构建相机变换矩阵 M = M_vp M_orth M_cam // 将它们乘在一起（注意顺序：先乘相机，再投影，最后视口） for each line segment (a_i, b_i) do // 遍历每条线段 p = M a_i // 变换点 a q = M b_i // 变换点 b drawline(x_p, y_p, x_q, y_q) // 画线
int main() { double fahrenheit; printf("This program converts fahrenheit to celsius and kelvin.\n"); printf("Enter a temperature in dgrees fahrenheit (q to quit):"); while(scanf("%lf", &fahrenheit) == 1) // continue executing loop if user enters valid number { Temperatures(fahrenheit); // convert fahrenheit to celsius and kelvin
//prompt for new input printf("Enter a temperatures in degrees fahrenheit (q to quit):"); } printf("Bye!\n"); }
do // get uppercase letter from user { printf("Enter an uppercases letter:"); scanf("%c", &uppercase_letter); }while (uppercase_letter < 'A'|| 'Z' < uppercase_letter);
int main() { char line[255]; int i = 0; // array printf("Enter a line to reerse:\n"); while (scanf("%c", &line[i]), line[i] != '\n') i++; for (; 0 <= i; i--) //previous loop leaves i in right postion printf("%c", line[i]); return 0; }
line[i] != ‘\n’ 的条件判断使得循环在用户输入的行中包含换行符之前继续执行。当用户按下 Enter 键时，输入的换行符会被检测到，并导致循环结束。
int main(void) { char ch; unsigned int ei_count = 0; bool e_flag = false;
printf("This program reads input and counts the number of times the\n" "sequence 'ei' occurs (case insensitive).\n"); printf("Enter input (%c to stop):\n", STOP);
while ((ch = getchar()) != STOP) { ch = tolower(ch); if (ch == 'e') e_flag = true; else if (ch == 'i') { if (e_flag) ei_count++; e_flag = false; } else e_flag = false;
***************************************************************** Enter the number corresponding to the desired pay rate or action: 1) $8.75/hr 2) $9.33/hr 2) $10.00/hr 4) $11.20/hr 3) quit *****************************************************************
int main() { bool exit_flag = false; int rate_option; double rate, hours, gross_pay, taxes,net_pay;
while (1) { printf("*****************************************************************\n"); printf("Enter the number corresponding to the desired pay rate or action:\n"); printf("1) $8.75/hr 2) $9.33/hr\n"); printf("3) $10.00/hr 4) $11.20/hr\n"); printf("5) quit\n"); printf("*****************************************************************\n");
scanf("%d", &rate_option); switch (rate_option) { case 1: rate = RATE_1; break; case 2: rate = RATE_2; break; case 3: rate = RATE_3; break; case 4: rate = RATE_4; break; case 5: exit_flag = true; break; default: //invalid input flush_input_buffer(); printf("please enter an integer between 1 and 5.\n"); continue; // repeat main program loop }
if (exit_flag) break; //exit program
printf("Enter the number of hours worked in a week:"); while (scanf("%lf", &hours) != 1 || hours <= 0) { flush_input_buffer(); printf("please enter a positive number.\n"); printf("Enter number of hours worked in a week:"); }
while (1){ printf("What would you like to order?\n"); printf("a) artichoke b) beet c) carrot q) quit\n"); option = getchar(); switch(option) { case ('q'): printf("Bye.\n"); return 0; //exit program
case ('a'): //artichokes printf("How many pound of artichokes would you like to add?"); if (scanf("%f", &weight) == 1) artichokeWeight += weight; else { flush_input_buffer(); printf("Invalid input. Try again.\n"); continue; //repeat main program loop } break;
case ('b'): //beets printf("How many pounds of beets would you like to add?"); if (scanf("%f", &weight) == 1) beetWeight += weight; else { flush_input_buffer(); printf("Invalid input. Try again.\n"); continue; //repeat main program loop } break;
case ('c')://carrots printf("How many pounds of carrots would you like to add?"); if (scanf("%f", &weight) == 1) carrotWeight += weight; else { flush_input_buffer(); printf("Invalid input. Try again.\n"); continue; //repeat main program loop } break; default: printf("Invalid input. Try again.\n"); continue; //repeat main program loop } //calculate subtotal artichokePrice = artichokeWeight * ARTICHOKE_PRICE_PER_LB; beetPrice = beetWeight * BEET_PRICE_PER_LB; carrotWeight = carrotWeight * CARROT_PRICE_PER_LB; subtotal = artichokePrice + beetPrice + carrotPrice;
void copy_2dim_arr(int rows, int cols, double source[rows][cols], double target[rows][cols]) { // copy one two-dimensional array to another for (int i = 0; i < rows; i++){ for (int j = 0; j < cols; j++) target[i][j] = source[i][j]; } }
void print_2dim_arr(int rows, int cols, double arr[rows][cols]) { //print the contents of a two-dimensional array
for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) printf(" %10.3f ", arr[i][j]);
#define SIZE 10 void add_arrays(int *addend1, int *addend2, int *sum, int array_length);
int main() { //test add_arrays srand(time(NULL));
int array1[SIZE]; int array2[SIZE]; int sum[SIZE];
// initialize arrays with random ints for (int i = 0; i < SIZE; i++) { array1[i] = rand() % 20; array2[i] = rand() % 20; }
// get sum of arrays add_arrays(array1, array2, sum, SIZE);
//print arrays printf("%8s %8s %8s\n", "Array 1", "Array 2", "Sum"); for (int i = 0; i < SIZE; i++) printf("%8d %8d %8d\n", array1[i], array2[i], sum[i]);
return 0; }
void add_arrays(int *addend1, int *addend2, int *sum, int array_length) { // calculate elementwise sum of two arrays for (int *tar = sum; tar < sum + array_length; tar++, addend1++, addend2++) *tar = *addend1 + *addend2; }
void input_data(int rows, int columns, double array[][5]); double compute_row_average(double *array, int cols); double compute_array_average(int rows, int cols, double array[rows][cols]); double largest_vlue(int rows, int cols, double array[rows][cols]);
int main() { double data[ROWS][COLUMNS];
input_data(ROWS, COLUMNS, data);
//print row averages printf("Row Averages:\n"); for (int i = 0; i < ROWS; i++) { printf("\t Average for row %d: %3.f\n", i + 1, compute_row_average(data[i], COLUMNS)); }
//print array average printf("Average for entire array: %.3f\n", compute_array_average(ROWS,COLUMNS, data));
// print largest value printf("Maximum array value: %.3f\n", largest_vlue(ROWS, COLUMNS, data));
return 0; }
void input_data(int rows, int columns, double array[][5]) { printf("Enter 3 groups of 5 double values each:\n"); for (int i = 0; i < rows; i++) { printf("Grop %d:", i + 1); for (int j = 0; j < columns; j++) scanf("%lf", array[i] + j); } }
double compute_row_average(double *array, int cols) { double total = 0; for (int i = 0; i < cols; i++) total += array[i];
return total / cols; }
double compute_array_average(int rows, int cols, double array[rows][cols]) { double total = 0; for (int i = 0; i < rows; i++) for (int j = 0; j < cols; j++) total += array[i][j];
return total / (rows * cols); }
double largest_vlue(int rows, int cols, double array[rows][cols]) { double max = array[0][0]; for (int i = 0; i < rows; i++) for (int j = 0; j < cols; j++) if (array[i][j] > max) max = array[i][j];
void sort_ASCII(char *strings[], int n) { // sort array of string pointers by ASCII collating sequence
char *tmp;
for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) { if (strcmp(strings[i], strings[j]) > 0) { tmp = strings[i]; strings[i] = strings[j]; strings[j] = tmp; } } }
void sort_length(char *strings[], int n) { // sort array of string pointer by length
char *tmp;
// 冒泡排序 for (int i = 0; i < n - 1; i++) for (int j = i + 1; j < n; j++) { if (strlen(strings[i]) > strlen(strings[j])) { tmp = strings[i]; strings[i] = strings[j]; strings[j] = tmp; } } }
int fwlen(char *string) { // return length of first word of string
int length = 0;
// skip leading whitespace while (isspace(*string)) string++;
// count first word length while (!isspace(*string)) { length++; string++; } return length; }
void sort_firstword_length(char *strings[], int n) { // sort array of string pointers by ASCII collating sequence
char *tmp;
for (int i = 0; i < n; i++) for (int j = i + 1; j < n; j++) { if (fwlen(strings[i]) > fwlen(strings[j])) { tmp = strings[i]; strings[i] = strings[j]; strings[j] = tmp; } } }
char * get(char *string, int n) { // wrapper for fgets that repalces first newline with null
char *ret_val = fgets(string, n, stdin); while (*string != '\0') { if (*string == '\n') *string = '\0'; string++; } return ret_val; }
void print_menu(void) { puts("Choose an option: "); puts("(o) Print strings in original order."); puts("(a) Print strings in ASCII collating sequence."); puts("(l) Print strings ordered by length."); puts("(f) Print strings ordered by length of the first word."); puts("(q) Quit."); puts(""); puts("Enter a character: "); }
int sum(const int ar[], int n); /* 函数原型 */ int sum(const int ar[], int n) /* 函数定义 */ { int i; int total = 0; for( i = 0; i < n; i++) total += ar[i]; return total; }
下面是一个类函数宏： #define PSQR(X) printf("The square of X is %d.\n", ((X)*(X))); 假设这样使用宏： PSQR(8); 输出为： The square of X is 64. C允许在字符串中包含宏参数。在类函数宏的替换体中，#号作为一个预处理运算符，可以把记号转换成字符串。例如，如果x是一个宏形参，那么#x就是转换为字符串”x”的形参名。这个过程称为字符串化（stringizing）。
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/* subst.c -- 在字符串中替换 */ #include <stdio.h> #define PSQR(x) printf("The square of " #x " is %d.\n",((x)*(x))) int main(void) { int y = 5; PSQR(y); PSQR(2 + 4); return 0; } 该程序的输出如下： The square of y is 25. The square of 2 + 4 is 36.
ag -g <File Name> # 类似于 find . -name <File Name> ag -i PATTERN # 忽略大小写搜索含PATTERN文本 ag -A [number] PATTERN #搜索含PATTERN文本，并显示匹配内容之后的n行文本，例如：ag -A 5 abc会显示搜索到的包含abc的行以及它之后5行的文本信息。 ag -B [number] PATTERN #搜索含PATTERN文本，并显示匹配内容之前的n行文本 ag -C [number] PATTERN #搜索含PATTERN文本，并同时显示匹配内容以及它前后各n行文本的内容。 ag --ignore-dir <Dir Name> #忽略某些文件目录进行搜索。 ag -w PATTERN #全匹配搜索，只搜索与所搜内容完全匹配的文本。 ag --java PATTERN #在java文件中搜索含PATTERN的文本。 ag --xml PATTERN #在XML文件中搜索含PATTERN的
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典型视图体积是一个边长为二、以原点为中心的立方体。
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为了任意查看，我们需要将要存储的点转换到“合适”的坐标系统。在这种情况下，它的原点为 e，并且坐标偏移以 uvw 表示。
点 $(2, 1)$ 应用了一个“平移 $(-1, 0)$”的变换。右上角的图是当我们把这个变换看作物理运动（点在动）时的心理图像，而右下角的图是当我们把这个变换看作坐标改变（在此例中是坐标原点的移动）时的心理图像。图中那个虚构的边界框仅仅是一种示意手段，在两种情况下，坐标轴和点的相对位置实际上是完全相同的。
点 p 可以用（这两个）坐标系中的任意一个来表示。
转换标准.png)
转换说明.png)
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