===== Transformation: Twisting around z-axis =====
**Definition**: inverse mapping\\
t = (z-z1)/(z2-z1)\\
theta = (1-t)*theta1 + t*theta2\\
x'=x*cos(theta)+y*sin(theta)\\
y'=-x*sin(theta)+y*cos(theta)\\ 

**Call**: hfTwistZ(xt,z1,z2,theta1,theta2);

**Parameters**:

xt - point coordinates array to be changed

z1, z2 - end points of z-interval

theta1, theta2 - rotation angles in radians for end points

**Test file**: [[http://hyperfun.org/twist.hf|twist.hf]]

===== Transformation: Twisting around y-axis =====
**Definition**: inverse mapping\\
t = (y-y1)/(y2-y1)\\
theta = (1-t)*theta1 + t*theta2\\
z'=z*cos(theta)+x*sin(theta)\\
x'=-z*sin(theta)+x*cos(theta)\\

**Call**: hfTwistY(xt,z1,z2,theta1,theta2);

**Parameters**:

xt - point coordinates array to be changed

z1, z2 - end points of z-interval

theta1, theta2 - rotation angles in radians for end points

**Test file**: [[http://hyperfun.org/twist.hf|twist.hf]]

===== Transformation: Twisting around x-axis =====
**Definition**: inverse mapping\\
t = (x-x1)/(x2-x1)\\
theta = (1-t)*theta1 + t*theta2\\
y'=y*cos(theta)+z*sin(theta)\\
z'=-y*sin(theta)+z*cos(theta)\\ 

**Call**: hfTwistX(xt,z1,z2,theta1,theta2);

**Parameters**:

xt - point coordinates array to be changed

z1, z2 - end points of z-interval

theta1, theta2 - rotation angles in radians for end points

**Test file**: [[http://hyperfun.org/twist.hf|twist.hf]]