Cairo 图形指南 (9) —— 变换

LiYanrui posted @ Apr 06, 2010 11:12:45 PM in 程序设计 with tags Cairo gtk , 12357 阅读

这一篇讲述变换(Transformation) 仿射变换是由一些线性变换与平移构成的。线性变换可以写为单个矩阵的形式。旋转是让一个刚体绕一点运动的变换。缩放变换是让物体的形状扩大与减小,并且在各个方向上的缩放因子都相同。平移变换将每个点沿着指定的方向移动常量距离。错切对于给定轴线,沿垂直于它的方向对物体进行移动的变换,并且在轴线的一侧的移动距离大于另一侧。

——上述内容来自维基百科全书

平移

下面这个例子演示了一个简单的平移变换。

#include <cairo.h>
#include <gtk/gtk.h>


static gboolean
on_expose_event(GtkWidget *widget,
    GdkEventExpose *event,
    gpointer data)
{
  cairo_t *cr;

  cr = gdk_cairo_create (widget->window);

  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 20, 20, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);

  cairo_translate(cr, 100, 100);

  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 20, 20, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);

  cairo_destroy(cr);

  return FALSE;
}


int main(int argc, char *argv[])
{
  GtkWidget *window;

  gtk_init(&argc, &argv);

  window = gtk_window_new(GTK_WINDOW_TOPLEVEL);

  g_signal_connect(window, "expose-event",
      G_CALLBACK (on_expose_event), NULL);
  g_signal_connect(window, "destroy",
      G_CALLBACK (gtk_main_quit), NULL);

  gtk_window_set_position(GTK_WINDOW(window), GTK_WIN_POS_CENTER);
  gtk_window_set_default_size(GTK_WINDOW(window), 300, 230); 
  gtk_widget_set_app_paintable(window, TRUE);

  gtk_widget_show_all(window);

  gtk_main();

  return 0;
}

这个例子先是画了个矩形,然后将它平移并绘制出平移结果。

 cairo_translate(cr, 100, 100);

cairo_translate() 函数可通过平移用于空间的原点来修改当前的变换矩阵。在这个示例中,是将原点沿水平和竖直方向平移了 100 个单位长度。

旋转

下面这个例子演示了一个简单的旋转变换。

#include <cairo.h>
#include <gtk/gtk.h>
#include <math.h>


static gboolean
on_expose_event(GtkWidget *widget,
    GdkEventExpose *event,
    gpointer data)
{
  cairo_t *cr;

  cr = gdk_cairo_create (widget->window);

  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 20, 20, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);

  cairo_translate(cr, 150, 100);
  cairo_rotate(cr, M_PI/2);

  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 20, 20, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);

  cairo_destroy(cr);

  return FALSE;
}


int main(int argc, char *argv[])
{
  GtkWidget *window;

  gtk_init(&argc, &argv);

  window = gtk_window_new(GTK_WINDOW_TOPLEVEL);

  g_signal_connect(window, "expose-event",
      G_CALLBACK (on_expose_event), NULL);
  g_signal_connect(window, "destroy",
      G_CALLBACK (gtk_main_quit), NULL);

  gtk_window_set_position(GTK_WINDOW(window), GTK_WIN_POS_CENTER);
  gtk_window_set_default_size(GTK_WINDOW(window), 300, 230); 
  gtk_widget_set_app_paintable(window, TRUE);

  gtk_widget_show_all(window);

  gtk_main();

  return 0;
}

这个例子先是画了个矩形,然后对它进行了平移和旋转变换,并绘制出变换结果。

 cairo_translate(cr, 150, 100);
 cairo_rotate(cr, M_PI/2);

首先对用户空间的原点进行平移,然后再围绕它旋转 180°。注意:旋转角度是弧度,而非角度。

缩放

下面这个例子演示了一个对象的缩放变换。(作者还真是沉闷阿,相同的句式连用了 n 次,这个可怜的矩形被折腾的痛苦不堪!)

#include <cairo.h>
#include <gtk/gtk.h>


static gboolean
on_expose_event(GtkWidget *widget,
    GdkEventExpose *event,
    gpointer data)
{
  cairo_t *cr;

  cr = gdk_cairo_create (widget->window);

  cairo_save(cr);
  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 20, 30, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);
  cairo_restore(cr);

  cairo_save(cr);
  cairo_translate(cr, 130, 30);
  cairo_scale(cr, 0.7, 0.7);

  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 0, 0, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);
  cairo_restore(cr);

  cairo_save(cr);
  cairo_translate(cr, 220, 30);
  cairo_scale(cr, 1.5, 1.5);

  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 0, 0, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);
  cairo_restore(cr);

  cairo_destroy(cr);

  return FALSE;
}


int main(int argc, char *argv[])
{
  GtkWidget *window;

  gtk_init(&argc, &argv);

  window = gtk_window_new(GTK_WINDOW_TOPLEVEL);

  g_signal_connect(window, "expose-event",
      G_CALLBACK (on_expose_event), NULL);
  g_signal_connect(window, "destroy",
      G_CALLBACK (gtk_main_quit), NULL);

  gtk_window_set_position(GTK_WINDOW(window), GTK_WIN_POS_CENTER);
  gtk_window_set_default_size(GTK_WINDOW(window), 360, 140); 
  gtk_widget_set_app_paintable(window, TRUE);

  gtk_widget_show_all(window);

  gtk_main();

  return 0;
}

这次的例子是用指定的缩放因子,把初始的矩形变的小了点,然后又把它变的大了点。

 cairo_save(cr);
 ...
 cairo_restore(cr);

若对初始的矩形完成两次缩放操作,需要将初始的变换矩阵保存一下,这个可通过 cairo_save() 和 cairo_restore() 函数来实现。

 cairo_translate(cr, 130, 30);
 cairo_scale(cr, 0.7, 0.7);

这里首先将用户空间的原点平移了一下,然后又开始用 0.7 作为因子进行缩放变换。

 

错切

在下面的示例中,我们来实现错切变换。

#include <cairo.h>
#include <gtk/gtk.h>


static gboolean
on_expose_event(GtkWidget *widget,
    GdkEventExpose *event,
    gpointer data)
{
  cairo_t *cr;
  cairo_matrix_t matrix;

  cr = gdk_cairo_create (widget->window);

  cairo_save(cr);
  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 20, 30, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);
  cairo_restore(cr);

  cairo_save(cr);
  cairo_translate(cr, 130, 30);
  cairo_matrix_init(&matrix,
      1.0, 0.5,
      0.0, 1.0,
      0.0, 0.0);

  cairo_transform (cr, &matrix);

  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 0, 0, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);
  cairo_restore(cr);

  cairo_save(cr);
  cairo_translate(cr, 220, 30);
  cairo_matrix_init(&matrix,
      1.0, 0.0,
      0.7, 1.0,
      0.0, 0.0);

  cairo_transform(cr, &matrix);

  cairo_set_source_rgb(cr, 0.6, 0.6, 0.6);
  cairo_rectangle(cr, 0, 0, 80, 50);
  cairo_stroke_preserve(cr);
  cairo_set_source_rgb(cr, 1, 1, 1);
  cairo_fill(cr);
  cairo_restore(cr);

  cairo_destroy(cr);

  return FALSE;
}


int main(int argc, char *argv[])
{
  GtkWidget *window;

  gtk_init(&argc, &argv);

  window = gtk_window_new(GTK_WINDOW_TOPLEVEL);

  g_signal_connect(window, "expose-event",
      G_CALLBACK(on_expose_event), NULL);
  g_signal_connect(window, "destroy",
      G_CALLBACK(gtk_main_quit), NULL);

  gtk_window_set_position(GTK_WINDOW(window), GTK_WIN_POS_CENTER);
  gtk_window_set_default_size(GTK_WINDOW(window), 360, 140); 
  gtk_widget_set_app_paintable(window, TRUE);

  gtk_widget_show_all(window);

  gtk_main();

  return 0;
}

这份示例代码实现了两次错切变换。对于错切变换,没有特定的函数,必须使用矩阵来实现。

 cairo_matrix_t matrix;

这个 cairo_matrix 是存储仿射变换的数据结构。 

 cairo_matrix_init(&matrix,
    1.0, 0.5,
    0.0, 1.0,
    0.0, 0.0);

 cairo_transform (cr, &matrix);

这一变换的数学形式可表示为:

[tex]
\begin{bmatrix}x_{new}\\ y_{new}\\ 1.0\end{bmatrix}=\begin{bmatrix}
{1.0 & 0.0 & 0.0}\\
{0.5 & 1.0 & 0.0}\\
{0.0 & 0.0 & 1.0}
\end{bmatrix}\begin{bmatrix}x\\ y\\ 1.0\end{bmatrix}
[/tex]

 cairo_matrix_init(&matrix,
     1.0, 0.0,
     0.7, 1.0,
     0.0, 0.0);

 cairo_transform(cr, &matrix);

 

这一变换的数学形式可表示为:

[tex]
\begin{bmatrix}x_{new}\\ y_{new}\\ 1.0\end{bmatrix}=\begin{bmatrix}
{1.0 & 0.7 & 0.0}\\
{0.0 & 1.0 & 0.0}\\
{0.0 & 0.0 & 1.0}
\end{bmatrix}\begin{bmatrix}x\\ y\\ 1.0\end{bmatrix}
[/tex]

 

椭圆

下面的这个例子,画了一个灰常复杂的形状,它由一串旋转的椭圆形成。

#include <cairo.h>
#include <gtk/gtk.h>

static gboolean
on_expose_event(GtkWidget *widget,
    GdkEventExpose *event,
    gpointer data)
{
  cairo_t *cr;

  cr = gdk_cairo_create(widget->window);

  gint width, height;
  gtk_window_get_size(GTK_WINDOW(widget), &width, &height); 

  cairo_set_line_width(cr, 0.5);
  cairo_translate(cr, width/2, height/2);
  cairo_arc(cr, 0, 0, 120, 0, 2 * M_PI);
  cairo_stroke(cr);

  gint i;

  cairo_save(cr);
  for ( i = 0; i < 36; i++) {
      cairo_rotate(cr, i*M_PI/36);
      cairo_scale(cr, 0.3, 1);
      cairo_arc(cr, 0, 0, 120, 0, 2 * M_PI);
      cairo_restore(cr);
      cairo_stroke(cr);
      cairo_save(cr);
  }

  cairo_destroy(cr);

  return FALSE;
}


int main(int argc, char *argv[])
{

  GtkWidget *window;

  gtk_init(&argc, &argv);

  window = gtk_window_new(GTK_WINDOW_TOPLEVEL);

  g_signal_connect(G_OBJECT(window), "expose-event",
      G_CALLBACK(on_expose_event), NULL);
  g_signal_connect(G_OBJECT(window), "destroy",
      G_CALLBACK(gtk_main_quit), NULL);

  gtk_window_set_position(GTK_WINDOW(window), GTK_WIN_POS_CENTER);
  gtk_window_set_default_size(GTK_WINDOW(window), 350, 250); 

  gtk_widget_set_app_paintable(window, TRUE);
  gtk_widget_show_all(window);

  gtk_main();

  return 0;
}
 cairo_translate(cr, width/2, height/2);
 cairo_arc(cr, 0, 0, 120, 0, 2 * M_PI);
 cairo_stroke(cr);

在 GTK+ 的窗口中间,绘制了一个圆,它是那些椭圆的边界圆。

 

 cairo_save(cr);
 for ( i = 0; i < 36; i++) {
     cairo_rotate(cr, i*M_PI/36);
     cairo_scale(cr, 0.3, 1);
     cairo_arc(cr, 0, 0, 120, 0, 2 * M_PI);
     cairo_restore(cr);
     cairo_stroke(cr);
     cairo_save(cr);
 }

沿着边界圆画 36 个椭圆。椭圆可用圆的缩放变换而获得。旋转这个椭圆,这样就创建了一个有趣的形状。

 

星星

下面的示例绘制了一个又旋转又缩放的星星,可惜不会发光呃。

#include <cairo.h>
#include <gtk/gtk.h>
#include <math.h>

int points[11][2] = { 
    { 0, 85 }, 
    { 75, 75 }, 
    { 100, 10 }, 
    { 125, 75 }, 
    { 200, 85 },
    { 150, 125 }, 
    { 160, 190 },
    { 100, 150 }, 
    { 40, 190 },
    { 50, 125 },
    { 0, 85 } 
};


static gboolean
on_expose_event(GtkWidget *widget,
    GdkEventExpose *event,
    gpointer data)
{
  cairo_t *cr;

  static gdouble angle = 0;
  static gdouble scale = 1;
  static gdouble delta = 0.01;

  gint width, height;
  gtk_window_get_size(GTK_WINDOW(widget), &width, &height);

  cr = gdk_cairo_create(widget->window);

  cairo_set_source_rgb(cr, 0, 0.44, 0.7);
  cairo_set_line_width(cr, 1);

  cairo_translate(cr, width / 2, height / 2 );
  cairo_rotate(cr, angle);
  cairo_scale(cr, scale, scale);

  gint i;

  for ( i = 0; i < 10; i++ ) {
      cairo_line_to(cr, points[i][0], points[i][1]);
  }

  cairo_close_path(cr);
  cairo_fill(cr);
  cairo_stroke(cr);

  if ( scale < 0.01 ) {
      delta = -delta;
  } else if (scale > 0.99) {
      delta = -delta;
  }

  scale += delta;
  angle += 0.01;

  cairo_destroy(cr);

  return FALSE;
}

static gboolean
time_handler (GtkWidget *widget)
{
  if (widget->window == NULL) return FALSE;
  gtk_widget_queue_draw(widget);
  return TRUE;
}


int main(int argc, char *argv[])
{

  GtkWidget *window;

  gtk_init(&argc, &argv);

  window = gtk_window_new(GTK_WINDOW_TOPLEVEL);

  gtk_widget_add_events (window, GDK_BUTTON_PRESS_MASK);

  g_signal_connect(window, "expose-event",
      G_CALLBACK(on_expose_event), NULL);
  g_signal_connect(window, "destroy",
      G_CALLBACK(gtk_main_quit), NULL);

 
  gtk_window_set_position(GTK_WINDOW(window), GTK_WIN_POS_CENTER);
  gtk_window_set_title(GTK_WINDOW(window), "star");
  gtk_window_set_default_size(GTK_WINDOW(window), 400, 300); 
  gtk_widget_set_app_paintable(window, TRUE);

  g_timeout_add(10, (GSourceFunc) time_handler, (gpointer) window);  

  gtk_widget_show_all(window);

  gtk_main();

  return 0;
}

在这个示例中,画了一颗星星,然后平移它,旋转它,缩放它。

 cairo_translate(cr, width / 2, height / 2 );
 cairo_rotate(cr, angle);
 cairo_scale(cr, scale, scale 

先将星星平移到窗口中间,旋转它,缩放它。(作者还真不是一般的罗嗦)

  for ( i = 0; i < 10; i++ ) {
      cairo_line_to(cr, points[i][0], points[i][1]);
  }

  cairo_close_path(cr);
  cairo_fill(cr);
  cairo_stroke(cr);

画它!

 if ( scale < 0.01 ) {
     delta = -delta;
 } else if (scale > 0.99) {
     delta = -delta;
 }

这几行代码控制星星的缩放过程。

fds 说:
2013年8月07日 15:02

Cairo变换操作都是都是针对当前绘制图形,可以读取一个图形文件,然后对它进行变换操作么


登录 *


loading captcha image...
(输入验证码)
or Ctrl+Enter