Lines


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On Folien 1 there are what appears to be “two curved parallel lines” about 80 mm apart. The defence argued that these lines represent the top and bottom edge of a drinking glass of about 80 mm high – a glass such as your typical whisky tumbler.

linesgif

It is notable that none of the defence experts ever magnified and investigated the shape and curvature of the lines. Intentionally or unintentionally they only assumed the lines are both curved and parallel. Thus, they made their findings based on observations alone. Industry standards, such as ACE-V protocols, prohibit this. You must test and verify what you claim. (Click here to see how Zeelenberg determined the “curvature” of the bottom line.)

Let us look at some basic geometry. Since a round conical drinking glass is essentialy part of a cone, when you fold such a glass open, you will find that the top and bottom edges form part of full circles. By way of simple geometrical calculations the radii of these circles can be calculated from the known dimensions of any round and conical glass. So, if we feed the top and bottom diameters and the height of the glass into the programmed spreadsheet, it will give us the the radii of the circles. Therefore, we can see how the curves would look like.

The basic principle is that the radii of the circles are influenced by the difference between the top and bottom diameters. The closer they are to being the same, the straighter the lines would be. The bigger the difference, the more curved the lines would be (circles become smaller).

geometry

For the lines on Folien 1 to be representations of the top and bottom ends of a conical drinking glass, both lines need to be circular arcs (a circular arc is a circular curve which is part of a circle). The circles also need to share the same origin (epicentre). Therefore the two arcs need to be concentric.

Our conclusion is that the lines on Folien 1 are not circular arcs and that they are not a concentric unit. They cannot be representations of the top and bottom edges of a round conical drinking glass, as was argued by the defence experts.

Below we take a closer look at both the top and bottom lines. In our Lines Report we also give more background.


Admittedly the top line on Folien 1 has the appearance of a curve and it creates the idea of the edge of a conical drinking glass. This was one of the first things the defence experts would fall back on to support their drinking glass theory. On this page we will zoom in on this line and get behind the deceiving nature of it.

top_line1

Above: Because this line looks curved, the defence experts assumed that it represented the top edge of a conical drinking glass. They also said the bottom “line” is curved. We’ll look at the bottom “line” later. We agree and will concede that a circular curve can roughly fit through the average of the top line. Since there is significant smudging and thickening in the line it is not always clear from where to measure when you do regression plotting. So for now we are not concerned about whether a circular curve fits or not. For now we will look at the internal structure of the top line and ask the question if in terms of its physical construction it can indeed be a representation of the top edge of a conical drinking glass, or any drinking glass for that matter.

flake_full

Above: This is the part of the line above the “lip print”. Note the two straight segments (yellow and green lines). The green line is a straight segment of about 2.5 cm splitting off from the yellow line below it. The yellow line is a straight segment of about 3.5 cm. This is a substantial part of the whole line of about 9 cm.

flake_close

flake_large

 Above: A closer look. Two straight segments on top of each other.

top_line3

Above: What appears to be a curve is actually largely a straight segment (between red lines) with smudging and flaking above the line adding to the overall perception of a curve.

Let’s go more towards the middle of the line.

line_mid

Let’s zoom in to this area.

hairline

Above: Note the fine and dead straight hairline under the yellow line. Below is the image without the yellow line. Start asking yourself if a round and conical drinking glass can leave such straight and fine features.

hairline2

hairline_smudge

Above: See if you can spot the hairline. Note all the smudging above and below the clear straight feature.

hair_mid2

Above: Hairline extending towards the middle of the line.

If we go further to the left along the line, one will find another straight segment running from this hairline.

3rd_straight_segment

Let’s move further to the left, where we will find yet another dead straight feature.

furrowA

Above: Note the furrow in the line. Can a drinking glass’ edge leave such a furrow, or rather a DVD cover? What contributes to the curve is smudging below the straight top edge of the line matter. This was most possibly caused by rubbing and gliding of the folien when the folien was rubbed over the ridged edge of the DVD cover.

What it comes down to is that the top line comprises of about four straight segments joined by smudging. Smudging and flaking above and below the segments contribute to the construction of a curve. Yes, eventually it deflects above a baseline in a curve like manner and could therefore be seen as a “curve”, but by closer inspection of the nature and construction of the “curve” it clearly does not appear to be a curve made by a curved object such as the edge of a conical drinking glass. It is not an authentic curve. It is a mosaic of straight segments and smudges which together forms the appearance of a curve.

four_segments

So how was the curved line formed? As there are some variables, such as the quality powder used on the day, it is difficult to say for sure, but we can say with much certainty that rubbing played a significant role.

Clip of how sleeve moves

It is very important to keep in mind that the sleeve is moveable.

photo_hand_on_sleeve

As you rub with the left fingers over the edge there will be more contact between the folien and the ridge towards the right – this is why the line is thicker towards the right. More smudging happened in that area.

rub_new1

The pink line is the powder line on the ridge of the cover which would record on the folien. There would have been some accumulation of powder on the ridge or in the groove between the sleeve and the cover’s ridge. When the folien was pasted on before rubbing it started to pick up the powder – when it was rubbed with the fingers (blue) to paste the folien down more properly the folien slid unevenly over the edge – picking up more powder towards the right – adding to the smudging, thickening and curvature of the line. Contact is made as you smear the folien down – recording of the edge is therefore not necessarily regular.

rub_ridge_side

We are not saying that the folien “stretched” as such, but we must remember that on the folien is an oily layer. While it stuck firmly to the sleeve it would have slid easily over the rather thin ridge that had some powder on, the loose powder on the ridge also enhancing sliding.

rub_close

Let’s look closer. The pink against the ridge represents the powder that would have accumulated here against and on the ridge. When the folien is rubbed exponentially from left to right over the ridge it picks it up powder as it glides over the ridge.

What is important to keep in mind is that there is a MOVEABLE sleeve on the cover. Therefore the folien sticks on the sleeve and when then rubbed the part of the folien that overlaps the ridge slides slightly over the ridge while still sticking to the sleeve. This sleeve’s top edge most probably contributed to the formation of the hairlines and the various straight segments during the gliding process (due to rubbing over the edge) as it “buckled” around and slid under the rubbing.

After seeing this, it may be a good idea to look at this image again.

rub_new1

This process fits with Swartz’ explanation of how he would have pasted and rubbed the folien onto the DVD cover.

Let us just again look at the amount of smudging.

hairline_smudgeA

When you paste a folien around a drinking glass, the reasonable way would be to smear the folien around the glass, clockwise or anticlockwise. Or both. Even if you rub towards the top edge, the folien will not glide over the edge since the folien is stuck to the glass. It may fold over a bit and therefore minor smearing can possibly occur. However, the degree of smudging you get in the top line of Folien 1 highly suggest rubbing over the ridge of a DVD cover rather than over a rim of a glass. The degree to which a folien sticks onto the glass surface, which is not moveable, hampers significant smudging.

Clip of how folien sticks to glass

Watch the clip above. You can rub upward all you want – the folien will not move. It may bend over the rim at times and may cause a blotch here and there, but there will be no sliding that will cause significant smudging. The curvature in the folien pasted to a round glass prevents significant bending – compared to a flat folien pasted to a DVD cover.

glass_hang

When you paste a folien around a glass, you can indefinitely hang the glass on the folien like this without the glass falling off or moving one bit. It is not so much that the folien is terribly sticky, but the oily surface sticks well to glass and covers the full adhesive area. The important fact here is that the folien will not glide over the rim with upward rubbing. Smudging will be minimal.

Let’s for example look what Mr Wertheim’s top line looks like:

wert_lift1

It’s rather smooth with no irregular thickening or significant smudging. With this line in mind, let’s look at a significant part of the Folien 1 line again.

flake_closeA

This flaked segment is certainly not smooth and curved.

——————————

Conclusion: A conical drinking glass will leave two concentric curves on a lift. Therefore both these lines would be circular arcs. A glass’ rim has a smooth, concurrent and constantly curved trajectory. This needs to be reflected in the lines it would leave on a lift. The powder may not record concurrently but the nature of the line will show that the lift came from a glass’ rim.

If you look closer at the top line, it is clear that the line does not have a constantly curved (circular) trajectory. Yes, visually it may appear as a curve, but when you look closer you’ll find that the curve is made up of some straight segments – eventually forming a line that looks like a curve. A round conical glass, as proposed by the defence experts, cannot yield such straight segments. It simply can’t.

Then, the amount of smudging in the line suggests that the line was not made by the top rim of a drinking glass. When you paste a folien on a glass there is simply not enough movement of the folien permitted to cause this amount of smudging.

Thus, the top line is excluded as a line made by a conical drinking glass based on:

1. Due to the degree of smudging it is arguable from where you should measure to determine regression coordinates, but there is no evidence that the line is a circular arc, as it should have been had Folien 1 been a lift from a drinking glass. Especially the straight alignment of the line towards the left, rules this line out as circular curve. No circular curve no glass.

2. The curve comprises of about 4 straight segments. A round conical drinking glass cannot leave straight features on a lift. No constant circular curve no glass.

3. The amount of smudging is too much to suggest a drinking glass.

We admit that the line is certainly not generally “consistent” with what one would typically expect from a lift from a DVD cover, and it may never be reproduced as such. But it must be considered that some variables are involved. The quality of powder used on the day, the quality of the folien used, the state of the specific DVD cover, the way the lifter worked, etc. All these factors could have played a part in the formation of the “curved” line. And without having for example the specific powder or batch of folien, it would be senseless to try and reproduce the line. But we have convincingly shown the basic mechanisms at play and that it is indeed possible.

This furrow in the line goes a long way to actually suggest a DVD cover.

furrowA

If you had to take a guess – is this representative of a glass’ rim or rather of the furrow between the sleeve and the ridge of a DVD cover?

sleeve_cover

THE BOTTOM LINE

As we now look at the bottom line, we will ask two questions: 1) Can it be a representation of the bottom edge of either a conical or a cylindrical drinking glass, and 2) if it can be a representation of the bottom end (edge) of any type of object?

Just a quick recap: When you take a lift from a cylindrical glass (top and bottom diameters are even) you will find two straight and parallel lines on the lift. When you take a lift from a round conical glass (top diameter is bigger than the bottom one) you will get two concentric arcs (parallel circular curves) on the lift.

Although the top line is not really a curve but rather a compilation of straight lines, it is not consistent with the type of line the top edge of a cylindrical glass would leave. The defence experts also suggested a conical tumbler, and they highlighted the “two parallel curves” in support of this. Cylindrical drinking glasses are very scarce and in most cases there will be some difference between the top and bottom diameters. Therefore it is safe to exclude a cylindrical glass right away. A glass with for example a square top edge has never been argued, and this would be very evident in the line it would leave. So we can exclude such a glass as well. Hence we will continue to look at the possibility of a round conical glass only.

As we have seen further above, with a conical glass the top and bottom edges are circles. If you would “fold” a glass open, the top and bottom edges would be circular curves which are part of full circles. These two circles will have the same origin (epicentre).

When we consider the bottom line on Folien 1 as possibly a representation of a the bottom edge of a conical drinking glass, we need to ask:

1) Is the line a curve of any kind?

2) Is the line a circular curve? A circular curve is a curve with a constant radius. It is part of a circle.

3) Is the curve part of a concentric unit with the top line?

Before we continue, it is important to realise and agree that if the line is a representation of the bottom edge of a round conical drinking glass, it needs to be a circular arc and it needs to be concentric to the top line. It is not a matter of “maybe, maybe not”. Margin of error due to smudging and flaking could be granted but the average trajectory of the line must be circular and it needs to work as part of a concentric unit with the top line.

Let us look at one permutation of a set of curves and see how they fit on the lines of Folien 1.

wert_curves4A

Above is the curves that Mr Wertheim’s Glass #2 would leave. Dimensions: 82 mm high, 79 mm top dia, 64 mm bottom dia. His glass is a bit higher than the height the distance between the lines. Nevertheless, it gives an idea of typical curves and how the lines on Folien 1 should have looked liked more or less.

We realise that there are millions of permutations of curves. The smaller the bottom diameter becomes in relation to the top one, the smaller both circles become – in normal speak, the curves will be “more curved”. Equally, the closer the diameters become to being the same, the “straighter” the lines would become.

What is more important to note, however, is that irrespective of any permutation, no circular curve will ever fit on the bottom line. Even though it is visually clear that the bottom line is simply not a curve of any kind, we have performed regression analyses on the line.

lines_plotsA

From a common baseline we measured coordinates over 49 spread intervals of 1 mm. In order to ensure accuracy, this was done under magnification and measured with an electronic measurement tool.

After the data were fed into a regression calculator, the result showed that the bottom line is an extremely poor fit to a circular curve, as we can see below.

plot_graphA

Furthermore, this exercise also confirmed that the bottom line could therefore not form part of a concentric unit with the top line.

Thus, based on the nature of the line, the fact that it is not a circular curve, the bottom line on Folien 1 can be excluded as being a representation of the bottom edge of a drinking glass.

Before we move on to some other issues, let’s look at some photo’s of the bottom line.

bott_line3A

It is clear that the line is made up of some straight segments.

Now let’s look if the line can be a representation of the bottom edge of any object.

Let’s first look at the top edge quickly again.

hairline_smudgeB

What is especially noticeable in the top line is the amount of smudging. About 50% of the line was severely affected by smudging. This was due to rubbing over the top edge of the object, right? Now, if we have smudging in the top line because the folien stuck over the top edge, why would we not have smudging in the bottom line if the folien stuck over the bottom edge too?

glass_rubX

As the hand rubs over the top and bottom edges it creates smudging in the lines where the folien meets the edges. It may be very minimal but the folien bends over the edge during rubbing over the edge. If we look at the complete lack of smudging in the bottom line, are we to believe that only rubbing over the top edge took place and not the bottom? Why would you only rub over one end?

Let’s look at the top and bottom line together.

bott_flash

If we consider this for the moment to be the top and bottom edges of a drinking glass, we can grant that the top edge has a rim and the bottom not and therefore it may record the respective edges differently, but ask yourself why there is absolutely no smudging or flaking in the bottom line.

Let’s look at what Mr Zeelenberg’s lift’s bottom line looks like.

bottom_z

Flaking and smudging is very visible although the average of the line stays circular.

This flaking is because of the round bottom edge of the glass. As you rub the folien over the edge it will to varying degrees make contact further around the round edge, recording these flakings.

bott_downward_roll

There is absolutely no indication of any smudging or flaking in the bottom line of Folien 1, which would suggest that unlike the top line it does not suggest the edge of an object.

The kinks in the bottom line may suggest this type of irregular contact around the rounding of a glass, much as the flaking in Zeelenberg’s line. We must remember two things. The trajectory of the line is still not circular. Even if it was flaking, the line’s trajectory is not right. Also, if you compare it with the flaking in Zeelenberg’s line, you will note that you can still see the average line running through the flaking. It is as if the flakes are hanging from below this average line. The deflections in the Folien 1 line seems to be solid. If we look a the most noticeable deflection towards the right, one will note that the average line runs straight through a drop in the deflection area. This means that if that area was a flake, then the drop would have been right on the rounding of the glass, which is impossible. Gravity and capillary action would have pulled it onto the surface below. There is no indication that these deflections and kinks are flakes due to rubbing around an edge.

ave_line_drop

We must also consider that the shape of the line would to a great extent be indicative of the shape of the object. Can you think of an object with such a shape at its bottom end?

bott_edge_shape

Conclusion:

– The bottom line is not a curve and most certainly not a circular curve. This immediately excludes it as a representation of the bottom edge of a conical drinking glass.

– The bottom line is not part of a concentric unit with the top line. Considered separately and jointly with the top line, the bottom line cannot be from the bottom edge of a drinking glass.

– The lack of smudging and flaking in the line suggest that it is not a representation of the end or an edge of an object, or at least that no rubbing occurred over the end/edge.

– The shape of the line does not suggests the shape of the bottom egde of any reasonable object.

So, how was the bottom line most likely formed?

According to Const Swartz’ testimony, he received the fully dusted cover from Inspector Mariaan Booysens. He applied a first folien towards the bottom half of the folien. He removed it and found no good prints on it. He put it in his briefcase to discard later. He put a second folien on the top part of the DVD cover, with the folien sticking over the edge of the DVD cover. He removed this folien, saw good prints on it and marked it as Folien 1.

 

second_lift_rip

Above is a very simplistic explanation by way of an illustration. There are many variables. The quality of the powder, the way the foliens were pasted, the way the folien were removed, etc. But it illustrates the very basic principle. (The line of the cut corner of the first lift would not necessarily record on the second lift, as Swartz told that he would hold the folien here between his forefinger and thumb in order to remove it easier. Therefore it did not make contact with the plastic.)

The “line” is full of kinks most possibly because the first folien did not paste in a straight line initially. If you do not rub the folien fully along the top edge, it does not make proper and regular contact with the plastic and when you lift it, it will record the powder irregularly. Or it may be that the folien was not cut that well. It is standard practice that larger sheets of folien are cut into smaller pieces before use.


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