Topics in 3-D Geometry and the Hoof
Monique Craig The Epona Institute Luwex 2015
Perception The world is 3D but our perceptions may not always allow us to think and perceive in 3D as well as we would wish. The 3-D world is tricky!
2-D Images of a 3-D World • Anytime we talk about an image – on a page of a book, on a computer screen, or even the image we see with our eyes – it is a 2-D image. • What is a 2-D Image? It is a projection of the 3-D world onto a surface. • Let’s look at 3 different ‘projections’ – Perspective – Orthogonal – Radiographic
• A perspective projection This is how we usually see the 3-D world
• An orthogonal projection A mathematical idealization that does not occur in nature.
• A radiographic projection
Because the beam diverges after passing through the subject, the image on the DR detector (or film) is always magnified.
Calibration in Radiographs
This is incorrect length due to magnification in radiographic projection.
This is the true length.
Make sure your digital x-ray system is using calibration to obtain true lengths!
The Brain Constructs 3-D By looking at a 3-D shape from several vantage points, the brain can begin to piece together what kind of 3-D shape must exist in order to create the 2-D images that we see.
Perspective Effects
Camera about 30 cm from hoof.
Camera about 2 m from hoof.
This is the same hoof. The images were taken 13 seconds apart.
Does it look like the same hoof to you?
Perspective Effects
For a more accurate photo: Hold the camera at least 1 meter away from the hoof and zoom-in.
Asymmetry is another Difficult Subject
The circle is the simplest symmetric shape because only one number is needed to fully specify it: it’s diameter. As shapes become more asymmetric, they require more numbers to specify them, and that is more difficult for our brains to grasp.
Fit Curve to P3 Periphery A “3-parameter ellipse� fits the shape of the dorsal periphery of the pedal bone quite well.
Lower Leg Bones are Asymmetric The lateral side of the pedal bone is usually wider than the medial side. The blue dots are the locations of the tip of the frog projected orthogonally onto the P3 bone for 20 hooves in our study.
The Hoof is Asymmetric • The hoof and lower leg bones are nearly symmetric, and this has led to many assumptions of symmetry ... But actually, they are slightly asymmetric. (Lateral side almost always wider than medial side)
The Hoof is Asymmetric
Nothing New
I’m not telling you anything new: old German texts on farrierry show drawings of the hoof which we measured today – they knew the hoof was asymmetric!
Summary of Asymmetry from DP View
Hoof mimics bone‌
Medial side is steeper.
The Hoof is Asymmetric
This exaggerated cartoon shows that the medial hoof wall is steeper than the lateral hoof wall. The “length of wall” below the sole plane are of unequal lengths in order that the “sole plane” is level with ground.
A Mistake
If you trim the hoof to make the medial and lateral wall angles match (because you believe in symmetry) you will cause the “sole plane� to tilt to the lateral side instead of being parallel to the ground.
Caudal View Shows Asymmetry
Lower Leg Bones are Asymmetric The long pastern (P1) is asymmetric, which causes the rotational axis of the fetlock joint to tilt – it is lower on the lateral side.
Lower Leg Bones are Asymmetric
Rotation centers and joint rotation axes indicated with dashed lines.
Lower Leg Bones are Asymmetric
The Main Point: it is impossible to trim the hoof in such a way that the coffin-joint axis and the fetlock-joint axis are both parallel to the ground!
Capsule Twists and Flares Medial
Lateral
We all know that hoof capsules are subject to twists and flares for a number of reasons‌
Hoof Twists and Flares
Along with the general asymmetries that the average hoof displays, for any particular hoof there are additional “local asymmetries” that we call “flares” or “twists” or other terms.
Bone-Referenced Trim • We trim at the bottom of the hoof, but if we do so by only looking at the bottom of the hoof, we may be following flares and other distortions. Let’s locate the boney column at the closest location to the site of our trimming! Just at the coronary band, one can palpate and feel the “coronary gaps” which are related to the boney column. This is the closest place to the trim where the bone can be located.
Coronary Gaps relate to the Bone
Bone-Referenced Trim
These points are absolutely the most distal bone reference one can hope to find without radiography. This explains my interest in them.
“Coronary gaps” palpated and marked….
Front of the hoof capsule has been removed…
Projecting the coronary gaps‌.
Relationship to the bones and joint.
The “coronary gaps� projected orthogonally onto the sole
Bone-Referenced Trim If you have difficulty locating the Coronary Gaps, the next best bone reference are at the distal end of P1 where boney eminences can be easily palpated.
The collateral ligaments to navicular bone (2) attach to the navicular bone (1) and to the bony eminences near the distal end of the P1 bone (3).
Bone-Referenced Trim
The locations of the projected points (red dots) on the sole help you assess the twists and flares of the hoof you are working on.
Bone-Referenced Trim It is method of palpation based on anatomy. In contrast to methods based at looking at the sole and shape of the hoof walls. There are many suggested reference points and external cues (e.g Duckett’s dot, 50-50 balance, etc.) These have merits but at the same time any of these can be shown to have limits to their accuracy --- while they may be useful ‘on average’ they are not necessarily reliable on a particular horse. Only a method which palpates the bones for an individual horse can provide a means to attain a bone-referenced trim.
Here we show a shoe which is “set to the boney column” rather than “set to the flare”.
Don’t ‘Set the Shoe to a Flare’
Let’s consider flares…
Don’t ‘Set the Shoe to a Flare’
Image a hoof with a lateral flare…
Don’t ‘Set the Shoe to a Flare’
Here, the shoe (in blue) is “set to the flare”…
Don’t ‘Set the Shoe to a Flare’
Rather, you should “set the shoe to the boney column”…
Don’t ‘Set the Shoe to a Flare’
But often, you need to “Split the difference with nature”.
In image B, the shoe is improperly “set to the flare� !
The Problem is… You have to be pretty good at 3-D geometry to “project” the bone points you palpate onto the sole of the hoof! Which brings us back to wanting to learn & practice more about geometry…
And‌it is just the tip of the iceberg!
There is so much more to take into consideration!
For example…
Changeability of the hoof due to influences (weather, riding, etc)
( Same hoof over a period of 15 months )
The End Copyright 2015 The Epona Institute