reflection of a curve with respect to a plane

Hi, given a curve, i have to plot it's reflection respect a plane defined by a point and a vector.

The curve is: x=-1:0.2:10 and y=x.^2+2, the point and the vector that define the space are P=[2 2 2] and V=[0 0 1].

This is my code by now:

clc;

clear all;

x=-1:0.2:10;

y=x.^2+2;

P=[2 2 2];

V=[0 0 1];

z=zeros(1,56);

ONE=ones(1,56)

A=[x.',y.',z.',ONE.'];

I know that i have to find the distance of each point of the curve from the plane, but i can't find the right way to use the for cycle, i want to use the dot function for each row and than create the reflection matrix.Use this matrix to calculate the new coordinate for each point and create the new matrix made with the coordinate of the reflect curve.This is my cycle for,it's not right but i write for make my self clear about my idea:

for i=1:length(x)

A2{i}=A(i,:);

A2t=A2'

C=cell2mat(A2t)

dist=dot(C-P,V);

d=abs(dist);

T=[1 0 0 (2*d*0);0 1 0 (2*d*0);0 0 1 (2*d*1);0 0 0 1];

B=T*C'

F=[B 56]

end

[Torsten]

If [0 0 1] is the normal vector of the reflection plane, the reflected curve should simply be (x,y,4), shouldn't it ?

[Federico Cotugno]

i put that data for example, but i need to know how to write the code for this type of exercise for an university exam

[Torsten]

I'll assume that the length of V is 1.

For each point P of the curve, calculate the intersection of the plane with the line L: x = P + lambda*V.

Let this intersection point be Q and Q = P + lambda0*V.

The reflection point is then x + 2*lambda0*V.

[Federico Cotugno]

maybe i didn't make myself clear.This is a specific unversity assignment,i have to do it in that way,with the matrix of reflection.I just need to know how to make that foor loop work

[Federico Cotugno]

Answer 1

[Torsten]

x = -1:0.2:10;
y = x.^2 + 2;
z = zeros(size(x));
P = [2 2 2];
V = [0 0 1];
d = (P.' - [x;y;z]).' * V.';
Ps = [x;y;z] + 2*V.'*d.'

Ps = 3×56

-1.0000 -0.8000 -0.6000 -0.4000 -0.2000 0 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000 2.2000 2.4000 2.6000 2.8000 3.0000 3.2000 3.4000 3.6000 3.8000 4.0000 4.2000 4.4000 4.6000 4.8000 3.0000 2.6400 2.3600 2.1600 2.0400 2.0000 2.0400 2.1600 2.3600 2.6400 3.0000 3.4400 3.9600 4.5600 5.2400 6.0000 6.8400 7.7600 8.7600 9.8400 11.0000 12.2400 13.5600 14.9600 16.4400 18.0000 19.6400 21.3600 23.1600 25.0400 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000

[Federico Cotugno]

Thanks, ours prof told us to use the for loop,i don't get why if it was this simple.Thank you very much <3