Thoughts On Mat Layout

The easiest and most common mat layout is one with the widths of all four borders equal. If you are forcing a picture into a standard-sized frame, however, that’s not always possible. And then there’s the matter of bottom-weighted mats.

Bottom-Weighted Mats

Bottom-weighted mats, or mats with the bottom edge wider than the others, were introduced long, long ago. Some say that pictures centuries ago were hung very high on the wall and the bottom width of the mat was increased to compensate for the ‘distortion’ of that perspective. Unfortunately, that story makes no sense; top-weighting would be required to correct for the top being further from the viewer than the bottom. Another explanation involves the notion of a difference between the visual or optical center and the geometric center. Yet others claim it is to compensate for the drop of the mat in the frame due to tolerances necessary to account for expansion, etc. For whatever reason, bottom weighting could be seen as an attempt to fool your audience or overcome optical perceptions, whichever you prefer. As commonly practiced in “finer frame shops everywhere”, the bottom width is generally increased ¼” to 1″, depending on the size of the pictureref.

Using Standard Mats

But how would one incorporate bottom weighting while fitting an image into a standard-sized mat? For example, if the vertical difference between the hole size and mat size is greater than the horizontal difference, and assuming the left and right borders will be the same width, is it better to:

 
 AMake the top and bottom borders equal,
 BMake the top the same size as the left and the right and put all of the extra width on the bottom,
 CMake the bottom larger than the top by some fixed amount,
DMake the differences even more subtle by making the difference between the top border and the side borders the same as the difference between the top and bottom borders?

Let’s clarify your choices with an example. Suppose you want a 4″-high hole that’s 7″ wide in a standard 8″-high by 10″ mat. The horizontal difference between the mat size and the hole size is 10″ – 7″ = 3″, so if you want the left and right borders to be the same, each will be 3″ ÷ 2 = 1½”. The vertical difference between mat and hole size is 8″ – 4″ = 4″.

Choice AWould make the top and bottom borders the same, making them each 4″ ÷ 2 = 2″.
 
Choice BWould make the top 1½” like the left and right borders, leaving 4″ – 1½” = 2½” for the bottom border.
 
Choice CUses the customary bottom weighting, which the one reference I give above lists as ¼” for an 8″x10″ mat (personally, a ¼” bottom weight isn’t worth the trouble). That means the top border would be (4″ – ¼”) ÷ 2 = 1⅞” and the bottom would be ¼” more, or 2⅛” (notice as you check your work that 1⅞” + 2⅛” = 4″). Finally,
 
Choice DIs a tad more complicated. Let’s call the difference between the left or right border width and the top border width “d”, such that
 1½” + d = T (for top border width).

Then the bottom border (B) would be

T + d or (substituting the last expression for T)
(1½” + d) + d = 1½” + 2⋅d.

Since T + B = 4″, then (substituting for T and B)

(1½” + d) + (1½” + 2⋅d) = 4″, meaning
3″ + 3⋅d = 4″ or 3⋅d = 1″, meaning d = ⅓”,

so (substituting back into our equations for T and B)

T = 1½” + ⅓” = 15/6” and
B =15/6” + ⅓” = 21/6

(again noting that 15/6” + 21/6” = 4″) .
Mat Weights
Our Four Mat Choices (drawn to scale)

The choice you make would be an artistic decision, but I think A is the most common answer. Choice C could be used for traditional bottom-weighting, as in our example, or could be used for some other more artistic value. Technically, both Choices B and D are possible results of that equation. B would be exactly what you get when you want bottom-weighting and are not restricted to standard mats; it would work best if the resulting difference between the top and bottom borders is not too much greater than the customary bottom-weighting distances mentioned above. In our example, it yields 2½” for the bottom border, which is an inch larger than the other three borders and may just be too much.  In our example, C and D are very close, and remain close when we change the amount of weight in C from ¼” to ½” (as shown by the lighter blue opening).  D is more subtle than C, but may only be worth the effort when the difference between the left and top borders is small enough to fool somebody.  In other cases with different numbers, results may vary. 

With Larger Side Borders

If the horizontal difference between the hole size and the mat size is greater than the vertical difference, you could face up to the same number of choices as above, but you are working with less material for the top and bottom borders and I think it is usually better to keep things simple and make those borders equal.

Differing Left And Right Borders?

Do the vertical borders always need be the same size? Although I can’t say I’ve ever seen or read about different-sized side borders, I’m not convinced that uniformity is strictly required. For example, in photography, as in older art forms, there a “rule” of spaceref that says, among other things, that there should be plenty of space on the side of the subject into which it is looking. If you have a “perfectly” centered and close-cropped picture of your mother looking to your left, could a mat with a wider border on the left side create the space that’s lacking in the image?  Maybe you could even choose a mat color that is a pastel version of the background to her right (your left)? Maybe a contrasting outer mat could be added with traditional (identical) vertical borders.

 I present the above thoughts to give some background and (more importantly) stimulate your own creativity. If you think of other possibilities, I’d be thrilled to have you add them to the comments. Thank you!

How To Find The Area Of An Object Using Photoshop

There are mathematical or drafting programs that may do a better job of finding areas of all sorts of seemingly random two-dimensional shapes, and I may have used one or two of these as a student, but I haven’t had any of them on my computer for many moons. So when I recently needed to compare the size of the visible sun at different times during a solar eclipse so I could compare exposure levels, I was out of luck. But then there was Photoshop. I just finished this article about how to find an object’s area, and put it on our website at www.beehappygraphics.com/find-area.html, mainly because I mentioned the technique in an earlier blog post, and was about to mention it again in an article I promised about the challenges of our newest eclipse image.  This probably isn’t the most common task you will be doing, but when you need it, this can be handy.  Enjoy!

A Solution To Second Mat(h) Problem

Sadly, we had no winners to this contest. Here is a solution to that math problem:

There is more than one way to solve this problem, but we will be exploiting three different relationships. First, in preserving the aspect ratio, the length of the image (we’ll call L) is 11/2 times the width (W). L = 1.5W . Then, adding up the components making up the overall width of the mat, the image width (less two overlaps of 1/8“) plus two mat widths (M) would equal 16 inches. W - \frac{1}{4}" + 2M = 16" By the same token, the image length (less same overlaps) plus two mat widths would be 20 inches. L - \frac{1}{4}" + 2M = 20"

If you replace the L in the last equation with its W equivalent from the first equation, and then add 1/4” to both sides of both equations to combine constants, you are left with the following two equations to solve with two unknown variables:

\begin{array}{r c l} 1.5W & + 2M = & 20.25 \\ W & + 2M = & 16.25 \end{array}

From here you can use linear algebra (matrices) or algebraic manipulation to simplify until you are left with just one variable. For example, just subtracting the bottom equation from the top (subtracting the left sides separately from the right sides of each equation), you will wind up with

0.5W = 4

which means the image width is eight inches, which means its length is twelve inches, and the mat guide would be set to 41/8“.

What’s Next

I’ve come up with one more printing-inspired math problem, which I will share as soon as I master a new plug-in for this blog.  After that, I’m not sure.  Response has been weak, but the former teacher in me feels a need to keep pointing out opportunities to use some of this stuff you learned in school (or is it just to torment those students who were the most difficult – I’m not telling).  This isn’t really costing anything, and I give enough warning for the math-averse to stay clear.  Stay tuned.

A Second Practical Mat(h) Problem

OK, here’s another problem inspired by matting pictures.  Suppose you have an image that you want to put in a standard 16″ by 20″ mat.  You can print the image any size, but want to keep the original 2:3 aspect ratio (meaning that the length will always be 50% longer than the width so you won’t lose any of the image due to cropping).  You want the mat to be the same width on all four sides.  Although standard mats overlap the image by 1/4″, this is not a standard hole so I like to use a 1/8″ overlap (which would be riskier with borderless prints).  The first question is “How large should you print the picture?”  Mathematically, there is only one correct answer to this question.  Once you figure it out, how wide should I cut the mat (where do I set the mat guide on the mat cutter)?

Another Mat Problem
Another Mat Problem

The Prize

Email your answer to blogger@BeeHappyGraphics.com.  The first three correct answers will receive $7 off any print and another $7 off if you choose to frame (or gallery-wrap) the image. As before, I will publish some responses, but obviously not immediately. So that nobody dies from the suspense, we will put a one-month deadline on this offer. Prizes may be redeemed any time after the winners are announced.  Good luck!

Ideas For Shooting The Solar Eclipse In Miami With Phone Or Camera

I have some ideas for shooting the eclipse by either phone or SLR camera.  For those who haven’t heard, the next eclipse will be Monday, August 21st. In Miami, the eclipse will start around 1:30 pm, which is right after local apparent noon (when the sun crosses due south of us around 1:24 pm and is 77° above the horizon). The eclipse will last about three hours, by which time it will have reached an azimuth (compass bearing) of 261° and dropped to a height of 44°. At its peak just before 3 o’clock, it will be 64° above the horizon at a bearing of 243° (west-southwest). At that time, less than 1/5 of its diameter will be visible in South Florida, which means that about 22% of the sun’s area will still be showing, and the sun will still be a little less than 1/4 of its normal brightness (for lack of anything better at hand, I used Photoshop’s Count Tool to figure the sun’s brightnessHow).

Shooting With Your Phone

In the news, they mentioned that you could use your smartphone to view the eclipse, but they warned that if your phone wasn’t eclipsing the sun (directly between you and the sun, obstructing your direct view) you could get seriously hurt, and since there are no nerves inside your eyeball, you wouldn’t immediately know the damage that was done. For that reason, you may want to use it in selfie mode.  You may also want to wait until the eclipse is close to its peak (although I have taken some test shots of the sun with no apparent damage to my phone).  There are a few problems with this approach, however. For one thing, the glare from your phone’s glass surface and/or the bright sunlight could make the image on the phone hard to see. On the other hand, if you actually wanted pictures, having yourself (or something else) in the foreground could improve the composition of the photograph.  But-

  1. The resolution for the selfie camera may not be as great as on the regular camera. (I explain why bigger is better on the Bee Happy Graphics FAQ page).
  2. My selfie camera doesn’t have controls for flash, exposure, white balance, and other things; these features being listed in the order of their importance.

You will need fill flash on your foreground subject, and the flash will probably need to be less than two feet away to be effective.  But that means the camera is in regular (non-selfie) mode and both aiming and pushing the shutter button could be a pain.  A short timer, if your app has one, could be helpful in pushing the button.

Shooting With A Camera

First, you will need neutral density filters, not just for the proper exposure but unless you shoot in Live View mode it is more important that the filters can adequately protect you looking through the viewfinder.  For that, a 10-stop filter is not enough (but a 12-stop filter, if it existed, could be (at your leisure, you can check out the Bee Happy Graphics blog for another reason a 12-stop neutral-density filter would be better than a 10-stop). A 15 or 16-stop filter would be even better in this case. Focus on the horizon before attaching your filters and lock in your focus.

If using a zoom lens, begin as wide as possible; it is easier to find the sun before zooming and avoid the dangers of trying to peek around the camera.  You will need exactly the same focal length or amount of zoom that you needed when you took pictures of the moon. Most experts feel anything less than a 300mm lens is a waste of time. Remember that your shutter speed should be 1/(focal length x crop factor) or faster if you not using a tripod, but even with a tripod there may be no reason to go with less. The aperture (f-stop) setting is not critical since all the action is at infinity but should be small enough (large enough number) so that you can keep the ISO at its lowest value.

If you are planning to capture the whole eclipse in a sequential composite photograph, decide how many images you need, subtract one, and divide that number into 180 minutes (the duration of the eclipse). If you want a string of six suns in your picture, each picture will be 180/5 or 36 minutes apart. The camera will probably not be locked down to the tripod for the duration, but the focal length of the lens and other settings should be the same for the entire series.

The only way to get something in the foreground (for better composition), is to go for multiple exposures and combine them manually. At the designated time, take the sun shot and while the camera is strapped to the tripod, record your camera settings, remove the filters, change the settings as needed and shoot the foreground. For multiple exposure shots, they usually advise changing only the shutter speed, but I’m not sure it matters in this instance. If changing the shutter speed alone is not enough, I’d change the f-stop before changing the ISO. Now record the settings of the foreground shot so you can repeat as necessary. If you must change the focus for the foreground shot, be sure to refocus on the horizon before putting the filters back on. Return the camera settings to the sun shot values. You may now move the camera on the tripod to compose the next shot. I mentioned that the sun will be putting out only 1/4 of its normal light at the peak of the eclipse here in Miami. This means the exposure of your foreground shot will change by two f-stops. The exposure of your sun shots shouldn’t change.

Final Words

Since this is such a rare event, you may not want to put all of your eggs in one basket. This means changing the settings of your camera (bracketing, if you will, checking the histogram, and perhaps rechecking the focus), which may mean taking several sequences simultaneously and taking good notes.

I’ve discussed some of your options, with some of the pros and cons of each one.  While I try to cover the technical aspects, you are the artist and the compositional issues are all yours.  It might be a good idea to get up early tomorrow and get some moon shots just for practice.  The moon will be just a waning (shrinking) crescent.  Moonrise here in Miami will be 4:37 am tomorrow and 5:40 Sunday (sunrise is 6:56 both days).

Well, that’s about it.  Have fun, don’t look directly at the sun, and let me know how it worked out for you.  I’d even be willing to post some of your pictures (with adequate credits of course).

A Simple Mat(h) Problem

Interesting math problems have always seemed to jump out of the woodwork at me. Here’s a simple geometry problem inspired by mat cutting. You don’t need a mat cutter or mat cutting experience to solve this problem, however.

Starting with a regular 40″ by 60″ foam board, a 23″ (by 40″) slice had already been removed for another project (shown as the large black-hashed area on the left edge of the illustration). In the blue dashed lines of the illustration, I drew simple plans to cut out four standard 16″ by 20″ pieces, but then discovered that there were problems along the top edge requiring me to remove a one-inch strip (shown with red hash marks), leaving a piece of foam board 39″ high by 37″ wide.

Illustration for Mat(h) problemThe question is “How many 16″ by 20″ pieces can I still get out of this remaining foam board?”. One would make the cuts on their mat cutter with a razor-like blade, so you don’t have to worry about a kerf (the extra material removed by the width of the saw blade).

The seven best answers will receive $7 off any print and another $7 off if you choose to frame (or gallery-wrap) the image. I will publish some responses, but obviously not immediately. So that nobody dies from the suspense, we will put a two-month deadline on this offer. Prizes may be redeemed any time afterwards.  Good luck!

Another Method For Adjusting A Logan Precision Sander

We have a Logan Precision Sander Elite Model F200-2 disk sander for improving saw-cut miters for your picture frames to a “perfect 45°” after cutting the moulding to size on our miter saw. To maintain such perfection requires due diligence and occasional adjustment.

How Do You Know When It’s Time To Adjust Your Sander?

  1. You may notice that when you put your frames together, there is a small gap between the pieces of moulding either on the inside of all four corners or the outside of all four corner. If some corners have gaps on the inside and some have a gap on the outside, you have other problems.
picture frames showing that your sander needs adjusting
The sander used on the miters of these two frames needs to be adjusted. Note gaps in corners.

In the figures used in this article, the symptoms have been exaggerated for illustration purposes. If the condition of your sander gets this bad without you noticing, you may want to consider another profession or hobby.

  1. When you are comparing the lengths of opposite pieces, and you have them side by side with the miters face up and their back sides touching, you may notice by running your finger over the miter that they are the same length on one end of the miter but not the other, or that one piece of moulding is higher at one end of the miter and the other piece is higher at the other end.
Differences in the miter cuts of moulding
The differences (gaps) in the mitered ends of these pieces of moulding show that your sander needs adjusting
In either of these cases, it’s time to adjust your sander.

But What About The Miter Saw?

It may be true that the miter saw also needs adjustment, but that would have minimal impact on your frames, because even if the angle of the cut was wrong, the sander should correct that problem. Of course it would take more sanding to correct, which beside taking more time and effort could, in the worst case, result in your frame being too small, so it should periodically be checked and corrected according to the manufacturer’s instructions (I currently have no improvements or suggestions for that process). An indication that the miter saw needed adjustment would be if as you are sanding the miter, sawdust builds up on top of one side of the moulding faster than it accumulates on the other. If it takes too many revolutions of the sander to perfect the edge, that could also be a clue, or it could be time to change the sandpaper.

How To Adjust The Sander

On the last page of the 4-page manual (available at www.logangraphic.com) are simple instructions for that adjustment that should work well if you are willing to follow Step 1 and remove the sandpaper.
To see the Note click here.To hide the Note click here.
The full instructions are as follows: Adjustment 45°
  1. Remove sand paper
  2. Place the 45˚ square flat against the wheel and up against bar (Fig. 7). Look for gaps against the bar.
  3. Adjust the bar using adjustment wrench until gap disappears.
Figure 7 of F200-2 Manual
Figure 7 of F200-2 Manual
When I don’t remove the sandpaper disk the technique doesn’t work as well, so I’ve come up with an alternate set of instructions:
  1. Put miter cuts on both ends of two long scrap pieces of your widest moulding.
  2. When you sand a piece of moulding, each end will use a different side of the sander. Call one side of the sander “A” and the other “B”. As you sand the two pieces of moulding, mark the back of each end of each piece with the side of the sander used (A or B).
  3. Find a good right angle, either in a reliable carpenter’s square or using other methods.
  4. Flip one of the pieces of scrap moulding upside down so you can join Corner “A” on both pieces to make a 90˚ (right) angle. Flipping is very important*.
  5. Put one piece of moulding along one edge of the reference angle (carpenter’s square) and slide the reference toward the second moulding until it just touches at one end or the other (if it touches at both ends, you are finished with Side A – skip ahead to Step 7). Measure the error gap (I like millimeters only because they are so small) at the end of the moulding that’s away from the reference line. Then measure the length of that piece of scrap moulding (using the same units of measurement).
  6. The adjustment screw on my sander had 32 threads per inch, and it was 109 millimeters from the pivot point. Based on that, your multiplier will be 25,000.
    To see the Note click here.To hide the Note click here.
    I’ll do the math just in case your sander has different measurements so that you can substitute the real numbers in for mine at the proper places. One complete turn of the adjustment screw is 360° or 1/32” and there are 25.4 millimeters per inch, so the constant multiplier would be 109 mm * 360° per turn of screw * 32 threads per inch ÷ 25.4 mm per inch ÷ 2 errors = 24,718.11. We’ll say 25,000.
    Divide the error you measured in the last step by the length of the moulding that you measured and multiply by 25,000. Your result will be the number of degrees you need to turn the adjustment screw. If the error gap was at the corner, then the angle is too large and you have to turn the screw counterclockwise to back it out. Conversely, if the error gap was at the end of the moulding, then the angle is too small and you have to turn the adjustment screw clockwise to push it out more. After making the adjustment, you may want to retest by repeating the process by starting at Step 2 and resanding the same two corners just used. Before sanding, I recommend drawing a line all the way across the end of the moulding with a pen or marker and then sanding until the line completely disappears.
  7. Repeat this whole process (starting at Step 4) for the other two miters, labeled “B”. Remember, for these two you will be playing with the adjustment screw on the other side of the sander.
That’s all there is to it. Congratulations.
To see the Note click here.To hide the Note click here.

Math Warning: a quick note about trigonometry (OPTIONAL)!

This process was concerned with angles, not distances, but since angles are harder to measure with any precision we had to convert. When you take the ratio of the two perpendicular sides (the sides that are 90° apart) of a right triangle containing the angle you are interested in, that’s called the tangent of that angle, and you can have a good calculator app on your phone find it for you (for my Droid, I found RealCalc Plus by Quartic Software at the Play Store and was happy to pay $3.50. There are plenty of other options, though). The error angle you measured (indirectly) was actually twice as large as the real error. One problem is that the tangent curve is not generally a straight line, which means that the tangent of twice some angle is not the same as twice the tangent of that angle. That’s why the normal procedure would be to convert to angles, do the adding, subtracting, or multiplying, and then convert back to distances we can measure again. We were able to use the small angle exception, however. It turns out that for angles less than say 10°, the tangent curve IS pretty straight and the error introduced by taking our shortcut isn’t worth worrying about. That’s what we did, and that’s why the problem was so easy. That’s your math lesson of the day week month. Let’s get back to work.