背景：
赛勒斯·贝克(Cyrus Beck)是针对凸多边形制作的线裁剪算法。与Cohen Sutherland或Nicholl Le Nicholl不同，它允许对非矩形窗口进行剪裁。它还消除了科恩·萨瑟兰(Cohen Sutherland)所需的重复剪辑。
Input:
1. Convex area of interest
which is defined by a set of coordinates
given in a clockwise fashion.
2. vertices which are an array of coordinates:
consisting of pairs (x, y)
3. n which is the number of vertices
4. A line to be clipped
given by a set of coordinates.
5. line which is an array of coordinates:
consisting of two pairs, (x0, y0) and (x1, y1)
Output:
1. Coordinates of line clipping which is the Accepted clipping
2. Coordinates (-1, -1) which is the Rejected clipping
算法：
- 计算每个边缘的法线。
- 计算剪裁线的向量。
- 计算每个边缘一个顶点与剪切线的一个选定端点的差与边缘法线之间的点积(对于所有边缘)。
- 计算剪裁线的向量和边缘法线(对于所有边缘)之间的点积。
- 前一个点积除以后一个点积并乘以-1。这是“ t”。
- “ t”的值通过观察其分母(后乘积)而分类为(从所有边开始)进入或离开。
- 从每个组中选择一个值“ t”，并将其放入线的参数形式以计算坐标。
- 如果输入的“ t”值大于输出的“ t”值，则剪切线将被拒绝。
情况： _0.jpg)
- 情况1：该行部分位于剪切窗口内：
0 < tE < tL < 1 where tE is 't' value for entering intersection point tL is 't' value for exiting intersection point - 情况2：该线在窗口内有一个点或在窗口的两侧，或者相交点在该线的端点上：
0 ≤ tE ≤ tL ≤ 1 - 情况3：该行完全在窗口之外：
tL < tE
伪代码：
首先，计算要剪切的线的参数形式，然后遵循算法。
P0 - PEi P1 - P0Ni . (P0 - PEi)
Ni . (P1 - P0)
where i -> ith edge of the convex polygonNi . (P0 - PEi)
t = ------------------
-(Ni . (P1 - P0))实现：这是SFML C++图形库中上述步骤的实现。您也可以按任意键以取消剪切线，并按任意键以剪切线。
// C++ Program to implement Cyrus Beck
#include
#include
#include
#include
using namespace std;
using namespace sf;
// Function to draw a line in SFML
void drawline(RenderWindow* window, pair p0, pair p1)
{
Vertex line[] = {
Vertex(Vector2f(p0.first, p0.second)),
Vertex(Vector2f(p1.first, p1.second))
};
window->draw(line, 2, Lines);
}
// Function to draw a polygon, given vertices
void drawPolygon(RenderWindow* window, pair vertices[], int n)
{
for (int i = 0; i < n - 1; i++)
drawline(window, vertices[i], vertices[i + 1]);
drawline(window, vertices[0], vertices[n - 1]);
}
// Function to take dot product
int dot(pair p0, pair p1)
{
return p0.first * p1.first + p0.second * p1.second;
}
// Function to calculate the max from a vector of floats
float max(vector t)
{
float maximum = INT_MIN;
for (int i = 0; i < t.size(); i++)
if (t[i] > maximum)
maximum = t[i];
return maximum;
}
// Function to calculate the min from a vector of floats
float min(vector t)
{
float minimum = INT_MAX;
for (int i = 0; i < t.size(); i++)
if (t[i] < minimum)
minimum = t[i];
return minimum;
}
// Cyrus Beck function, returns a pair of values
// that are then displayed as a line
pair* CyrusBeck(pair vertices[],
pair line[], int n)
{
// Temporary holder value that will be returned
pair* newPair = new pair[2];
// Normals initialized dynamically(can do it statically also, doesn't matter)
pair* normal = new pair[n];
// Calculating the normals
for (int i = 0; i < n; i++) {
normal[i].second = vertices[(i + 1) % n].first - vertices[i].first;
normal[i].first = vertices[i].second - vertices[(i + 1) % n].second;
}
// Calculating P1 - P0
pair P1_P0
= make_pair(line[1].first - line[0].first,
line[1].second - line[0].second);
// Initializing all values of P0 - PEi
pair* P0_PEi = new pair[n];
// Calculating the values of P0 - PEi for all edges
for (int i = 0; i < n; i++) {
// Calculating PEi - P0, so that the
// denominator won't have to multiply by -1
P0_PEi[i].first
= vertices[i].first - line[0].first;
// while calculating 't'
P0_PEi[i].second = vertices[i].second - line[0].second;
}
int *numerator = new int[n], *denominator = new int[n];
// Calculating the numerator and denominators
// using the dot function
for (int i = 0; i < n; i++) {
numerator[i] = dot(normal[i], P0_PEi[i]);
denominator[i] = dot(normal[i], P1_P0);
}
// Initializing the 't' values dynamically
float* t = new float[n];
// Making two vectors called 't entering'
// and 't leaving' to group the 't's
// according to their denominators
vector tE, tL;
// Calculating 't' and grouping them accordingly
for (int i = 0; i < n; i++) {
t[i] = (float)(numerator[i]) / (float)(denominator[i]);
if (denominator[i] > 0)
tE.push_back(t[i]);
else
tL.push_back(t[i]);
}
// Initializing the final two values of 't'
float temp[2];
// Taking the max of all 'tE' and 0, so pushing 0
tE.push_back(0.f);
temp[0] = max(tE);
// Taking the min of all 'tL' and 1, so pushing 1
tL.push_back(1.f);
temp[1] = min(tL);
// Entering 't' value cannot be
// greater than exiting 't' value,
// hence, this is the case when the line
// is completely outside
if (temp[0] > temp[1]) {
newPair[0] = make_pair(-1, -1);
newPair[1] = make_pair(-1, -1);
return newPair;
}
// Calculating the coordinates in terms of x and y
newPair[0].firs
t
= (float)line[0].first
+ (float)P1_P0.first * (float)temp[0];
newPair[0].second
= (float)line[0].second
+ (float)P1_P0.second * (float)temp[0];
newPair[1].first
= (float)line[0].first
+ (float)P1_P0.first * (float)temp[1];
newPair[1].second
= (float)line[0].second
+ (float)P1_P0.second * (float)temp[1];
cout << '(' << newPair[0].first << ", "
<< newPair[0].second << ") ("
<< newPair[1].first << ", "
<< newPair[1].second << ")";
return newPair;
}
// Driver code
int main()
{
// Setting up a window and loop
// and the vertices of the polygon and line
RenderWindow window(VideoMode(500, 500), "Cyrus Beck");
pair vertices[]
= { make_pair(200, 50),
make_pair(250, 100),
make_pair(200, 150),
make_pair(100, 150),
make_pair(50, 100),
make_pair(100, 50) };
// Make sure that the vertices
// are put in a clockwise order
int n = sizeof(vertices) / sizeof(vertices[0]);
pair line[] = { make_pair(10, 10), make_pair(450, 200) };
pair* temp1 = CyrusBeck(vertices, line, n);
pair temp2[2];
temp2[0] = line[0];
temp2[1] = line[1];
// To allow clipping and unclipping
// of the line by just pressing a key
bool trigger = false;
while (window.isOpen()) {
window.clear();
Event event;
if (window.pollEvent(event)) {
if (event.type == Event::Closed)
window.close();
if (event.type == Event::KeyPressed)
trigger = !trigger;
}
drawPolygon(&window, vertices, n);
// Using the trigger value to clip
// and unclip a line
if (trigger) {
line[0] = temp1[0];
line[1] = temp1[1];
}
else {
line[0] = temp2[0];
line[1] = temp2[1];
}
drawline(&window, line[0], line[1]);
window.display();
}
return 0;
}
输出：
(102, 50) (240, 109)- 剪裁之前：
_1.jpg)
- 剪裁后：
_2.jpg)