我有一个2乘4矩阵coor
定义了四个点:飞机上一条线的(0,0)
,(a,0)
,(a, -b)
和(a-c, -b)
:
a<-3; b<-1; c<-1
coor <- matrix(0,2,4)
coor <- t(matrix(c(0,0, a,0, a,-b, a-c, -b), nrow=2));
我已经添加到coor
矩阵中,第3列是'1',以便在乘法中使用此矩阵。
coor <- cbind(coor, 1)
我需要1)将原点从(0,0)
转换到第四点,使用协调(a-c,-b)
和2)在角度alpha
上旋转线:
# translation matrix
I <- matrix(0,3,3); diag(I) <- 1
I[1, 3] <- -coor[4, 1]
I[2, 3] <- -coor[4, 2]
alpha = -pi/2
# rotation matrix
M <- matrix(c(cos(alpha), sin(alpha), 0,
-sin(alpha), cos(alpha), 0,
0, 0, 1), nrow=3)
coor1 <- matrix()
coor1 <- coor %*% I %*% M %*% solve(I)
两项操作的结果是:
> cbind(coor1[,1], coor1[,2])
[,1] [,2]
[1,] 0.00000e+00 0
[2,] 1.83691e-16 3
[3,] 1.00000e+00 3
[4,] 1.00000e+00 2
预期结果是:
> coor2 <- matrix(c(2,-1, 2,2, 3,2, 3,1),nrow=2); t(coor2);
[,1] [,2]
[1,] 2 -1
[2,] 2 2
[3,] 3 2
[4,] 3 1
原始点和结果的绘图如下。在图中,我将给定点分组在红线中,其中a,b,c是相应线段的长度。
plot(t(coor[1,]), t(coor[2,]), col='red', type= 'l', xlim=c(0,3), ylim=c(-1,3), xlab='x', ylab='y')
points(round(cbind(coor1[,1], coor1[,2]),2), col='green', type= 'l')
points(t(coor2), col='blue', type= 'l')
题。如何正确地使矩阵乘法coor %*% I %*% M %*% solve(I)
以便将第一个点从(0,0)
移动到(a-c, -b)
?
编辑。
Combining translation and rotation
完整代码:
a<-3; b<-1; c<-1
coor <- matrix(0,2,4)
coor <- t(matrix(c(0,0, a,0, a,-b, a-c, -b), nrow=2));
coor <- cbind(coor, 1)
# translation matrix
I <- matrix(0,3,3); diag(I) <- 1
I[1, 3] <- -coor[4, 1]
I[2, 3] <- -coor[4, 2]
alpha = -pi/2
# rotation matrix
M <- matrix(c(cos(alpha), sin(alpha), 0,
-sin(alpha), cos(alpha), 0,
0, 0, 1), nrow=3)
coor1 <- matrix()
coor1 <- coor %*% I %*% M %*% solve(I)
coor2 <- matrix(c(2,-1, 2,2, 3,2, 3,1),nrow=2)
plot(coor[,1], coor[,2], col='red', type= 'l', xlim=c(-3,6), ylim=c(-2,6), xlab='x', ylab='y')
points(x=coor1[,1], y=coor1[,2], col='green', type= 'l')
points(t(coor2), col='blue', type= 'l')
关于这个问题的答案:
a <- 3; b <-1 ; c <- 1
coor <- matrix(0, 2, 4)
coor <- t(matrix(c(0,0, a,0, a,-b, a-c, -b), nrow=2));
coor <- cbind(coor, 1)
alpha = -pi/2
coor1 <- matrix(0, 3, 3)
# new origin (x, y)
x <- coor[4,1]; y <- coor[4,2]
T <- matrix(0, 3, 3)
T <- matrix(c(cos(alpha), sin(alpha), x,
-sin(alpha), cos(alpha), y,
0, 0, 1), nrow=3);
coor1 <- coor %*% T
plot(coor[,1], coor[,2], col='red', type= 'l', xlim=c(0,3), ylim=c(-1,2), xlab='x', ylab='y')
points(round(cbind(coor1[,1], coor1[,2]),2), col='green', type= 'l')