### Grid, Plane and Fix Anchor Geometry Problem

Posted:

**Sun Feb 16, 2020 3:15 pm****Problem statement:**

you are given 4 coordinates of the points.

**Grid size:**X*Y (Both scalar parameters)

**Plane Size:**Px * Py (Both scalar parameters)

**Fixed point:**don't change the coordinate of the point.

GNx, No of plane on X axis= ceil(X/Px)

GNy, No of plane on Y axis= ceil(Y/Py)

this will generate the new grid of GNx*GNy.

Find the 4 coordinates of the new grid such that the position of the fixed point remains the same.

**Hint: Slope of all the sides will remain same after transformation.**=================================================================================

**Inputs :**

**Grid size:**Int X, Int Y

**Plane size:**Int Px, Int Py

**Points array :**

[0] (x0,y0)

[1] (x1,y1)

[2] (x2,y2)

[3] (x3,y3)

**Fixed Point index:**Int FixedPoint

=================================================================================

**Output Points array :**

[0] (Nx0,Ny0)

[1] (Nx1,Ny1)

[2] (Nx2,Ny2)

[3] (Nx3,Ny3)

*=================================================================================*

**project euler answer will be: "Nx0,Ny0,Nx1,Ny1,Nx2,Ny2,Nx3,Ny4"**

without rounding off up to 2 decimal points.without rounding off up to 2 decimal points.

**Sample Example 1:**

**Grid Size:**X*Y= 10*10

**plane size:**Px * Py = 2*2

**corner to fix:**0

**input points:**

[0]-20,20

[1]-20,-20

[2]20,20

[3]20,-20

GNx, No of plane on X axis= ceil(X/Px) = ceil (10/2) = 5

GNy, No of plane on Y axis= ceil(Y/Py) = ceil (10/2) = 5

so GNx*GNy = 5*5

**output points:**

[0]-20,20

[1]-20,-20

[2]20,20

[3]20,-20

*so the answer is: -20.00,20.00,-20.00,-20.00,20.00,20.00,20.00,-20.00*

In this example planes of 2x2 is perfectly accommodated in grid size of 10x10, so the points will remain the same.

=================================================================================

**calculate the values for the following:**

**Grid Size:**X*Y= 9*9

**plane size:**Px * Py = 6*6

**corner to fix:**0

**input points**

[0]-18,20

[1]-18,-20

[2]15,15

[3]15,-15

GNx, No of plane on X axis= ceil(X/Px) = ceil (9/6) = 2

GNy, No of plane on Y axis= ceil(Y/Py) = ceil (9/6) = 2

so GNx*GNy = 2*2

What are the output points for the above?