Enlargement without Maths

 Setting out an enlargement grid can be done without the mathematics of ratios.  It uses an old method of estimated interval size and angles relating to the ends of the estimation and the width of the design.  This gives the method in simple images.

     Start with your original design

Draw line at a shallow angle from one corner

Determine number of grid lines (say 10) along the bottom edge.  Choose a length approximately the size needed for the grid.  Mark out the number of divisions with dividers or compass on that slope.

Connect the final mark with the corner at the end of the line started on.  Place a right angle on that line.

   Fix a long straight edge under that right angle and fix it so it does not move

·        Transfer the marks on the sloped line to the edge of the image.

This gives ten equal divisions. Adjust the divider opening to the width of the division.

Use dividers with this opening to transfer the division size to the other edge.

Do this on all four edges if a rectangle.

Do the same process for the enlarged size.

Draw a slope

Estimate the size of the division.  Mark that estimate on the slope as for the original design.  Fix a right angle between the end of the slope marks and the corner of the design.  Fix the straight edge and mark off the divisions on the enlarged size.  Transfer these divisions with the new division opening of the dividers

Draw the grid.

Note where the design crosses the grid lines. Transfer marks onto the enlarged grid proportionally.  To avoid confusion, mark one line in at a time.

An intersection of the design line two thirds up the design grid vertical gets a mark two thirds up the corresponding enlarged vertical.  The same with horizontal grid lines.  Connect the dots one line at a time in pencil.  They can be altered later and erased once the final lines are inked in.

 

Enlarging Designs by Hand

Not everyone has easy access to enlarging copiers.  Even when they are available, large enlargement ratios produce distortions.  This presents a dilemma when a big enlargement is needed.  Is it necessary to redraw the whole design at a larger scale?  There is a way to enlarge a design without machines or needing to redraw the whole.  This is a description of how it can be done.

The old fashioned way to enlarge an image is to grid the smaller original.  This grid is normally made in squares of convenient size.  The grid size does not have to fit evenly into the dimensions of the original.  It is easier if the longest side has a size of grid that fits evenly into it.  This probably means there will be an uneven fit of the square grid on the other dimension.  This is not a big problem. 

The size of the grid is related to the amount of detail.  More detailed original images need smaller squares than images with less detail.  Detailed images may require a 1cm/0.375” square grid or less.  This is to ensure all the detail is included in the enlarged image.  A less detailed original may only need a 2.5cm/1.0” grid.

Also, bigger enlargements require more squares on the original than smaller enlargements.  If you are enlarging more than three times, you should be looking toward smaller squares for the grid.  This allows you to maintain the curves and angles more easily on the enlarged copy.  Smaller enlargements can have a larger grid size.  The relevance of the grid size becomes apparent when you set out the enlarged grid.

It is useful to use a set of dividers to ensure the repeated grid size is set out on the boundaries of the original image size.  Once set, the distance between the two points of the dividers remains constant as you “walk” them along the boundaries.  If you mark all four sides of the image with the dividers, you only need a straight edge to draw the grid lines.  I draw the lines in pencil. Then if I make any mistakes, I can erase the lines and set new ones.

On another piece of paper set out the new enlarged size boundaries.  If you have set the boundaries at the correct size relative to the original, the new grid should fit evenly into the long dimension.  Multiply the grid size on the original by the enlargement ratio.  This gives you the size of the enlargement grid.  Set your dividers to this and mark off the enlarged grid.

In fact, most of the time, the difference between the final enlarged and the original size determines the enlargement ratio.  To get this ratio, divide the enlarged size by the original size to get the ratio.  This ratio needs to be applied to the new grid size.  If it does not fit well, adjust the dividers to the required size and mark the length again.

Example:

·        The approved design is 10 by 15cm/ 4” by 6”

·        The final size is to be 60 by 91.5cm/ 24” by 36” (assuming your design is in the same proportions as the final size).

·        Assuming your design is of moderate detail, squares of 1cm/ 0.39” might be enough to capture the detail.  For more detail, smaller squares would be required.

·        To determine the size of the squares in the full size design, divide the final size by the design size.  I prefer to use the bottom side for this calculation, but either side will work. The bottom side of the full size is 60cm, and the design is 10cm. The division shows that the squares on the full size need to be in a ratio of 1:6.0. This means the squares on the full size need to be 6.0cm/ 2.4”.

·        If this appears to be too large a grid, the squares can be divided to capture more detail.

 

The next blog post will show how to divide the design and full size without using maths at all.

Having marked the edges of the design with the grid sizes, draw the grid across the design.  Do this in pencil, so the grid lines can be erased when the enlargement is completed. This will give intersections between the design lines and both the grids. 

Enlarging involves marking these intersections on the full size grid in proportional locations.  E.g., if on the design the intersection on the grid line is 2/3 up the grid square.  On the large one mark it also 2/3 up on the corresponding square. Do one line at a time to avoid confusion.  When as much of the line intersections as you want for that element are transferred, draw the line in on the full size.  There will need to be some adjustment when finished, so use a pencil for all these operations.

When satisfied with the look of the full size, ink in the lines and erase the grid and any unwanted lines. You now have a full size cartoon to work with. 

Manually enlarging a design is most useful when you do not have access to machines, and when the enlargement is more than two times.  Machines distort the lines at high magnifications and require checking and often redrawing of edges and various elements anyway.