如何实现图像2D转换（|物体旋转）

本文概述

我们必须围绕给定的枢轴点将对象旋转给定的角度, 然后打印新的坐标。
例子：

Input : {(100, 100), (150, 200), (200, 200), (200, 150)} is to be rotated about (0, 0) by 90 degrees Output : (-100, 100), (-200, 150), (-200, 200), (-150, 200)

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Input : {(100, 100), (100, 200), (200, 200)} is to be rotated about (50, -50) by -45 degrees Output : (191.421, 20.7107), (262.132, 91.4214), (332.843, 20.7107)

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为了旋转对象, 我们需要分别旋转图形的每个顶点。
将点P(x, y)绕原点旋转角度A, 我们得到一个点P'(x', y')。 x’和y’的值可以如下计算：

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【如何实现图像2D转换（|物体旋转）】我们知道,
x = rcosB, y = rsinB
x’ = rcos(A+B) = r(cosAcosB – sinAsinB) = rcosBcosA – rsinBsinA = xcosA – ysinA
y’ = rsin(A+B) = r(sinAcosB + cosAsinB) = rcosBsinA + rsinBcosA = xsinA + ycosA
旋转矩阵方程：-

// C program to rotate an object by // a given angle about a given point #include < math.h> #include < stdio.h> // Using macros to convert degree to radian // and call sin() and cos() as these functions // take input in radians #define SIN(x) sin(x * 3.141592653589 / 180) #define COS(x) cos(x * 3.141592653589 / 180) // To rotate an object void rotate( float a[][2], int n, int x_pivot, int y_pivot, int angle) { int i = 0; while (i < n) { // Shifting the pivot point to the origin // and the given points accordingly int x_shifted = a[i][0] - x_pivot; int y_shifted = a[i][1] - y_pivot; // Calculating the rotated point co-ordinates // and shifting it back a[i][0] = x_pivot + (x_shifted * COS(angle) - y_shifted * SIN(angle)); a[i][1] = y_pivot + (x_shifted * SIN(angle) + y_shifted * COS(angle)); printf ( "(%f, %f) " , a[i][0], a[i][1]); i++; } } // Driver Code int main() { // 1st Example // The following figure is to be // rotated about (0, 0) by 90 degrees int size1 = 4; // No. of vertices // Vertex co-ordinates must be in order float points_list1[][2] = { { 100, 100 }, { 150, 200 }, { 200, 200 }, { 200, 150 } }; rotate(points_list1, size1, 0, 0, 90); // 2nd Example // The following figure is to be // rotated about (50, -50) by -45 degrees /*int size2 = 3; //No. of vertices float points_list2[][2] = {{100, 100}, {100, 200}, {200, 200}}; rotate(points_list2, size2, 50, -50, -45); */ return 0; }

CPP

// C++ program to rotate an object by // a given angle about a given point #include < iostream> #include < math.h> using namespace std; // Using macros to convert degree to radian // and call sin() and cos() as these functions // take input in radians #define SIN(x) sin(x * 3.141592653589 / 180) #define COS(x) cos(x * 3.141592653589 / 180) // To rotate an object given as order set of points in a[] // (x_pivot, y_pivot) void rotate( float a[][2], int n, int x_pivot, int y_pivot, int angle) { int i = 0; while (i < n) { // Shifting the pivot point to the origin // and the given points accordingly int x_shifted = a[i][0] - x_pivot; int y_shifted = a[i][1] - y_pivot; // Calculating the rotated point co-ordinates // and shifting it back a[i][0] = x_pivot + (x_shifted * COS(angle) - y_shifted * SIN(angle)); a[i][1] = y_pivot + (x_shifted * SIN(angle) + y_shifted * COS(angle)); cout < < "(" < < a[i][0] < < ", " < < a[i][1] < < ") " ; i++; } } // Driver Code int main() { // 1st Example // The following figure is to be // rotated about (0, 0) by 90 degrees int size1 = 4; // No. of vertices // Vertex co-ordinates must be in order float points_list1[][2] = { { 100, 100 }, { 150, 200 }, { 200, 200 }, { 200, 150 } }; rotate(points_list1, size1, 0, 0, 90); // 2nd Example // The following figure is to be // rotated about (50, -50) by -45 degrees /*int size2 = 3; //No. of vertices float points_list2[][2] = {{100, 100}, {100, 200}, {200, 200}}; rotate(points_list2, size2, 50, -50, -45); */ return 0; }

输出如下：