Cusp: Request for opinions

[Scott]

Cusp:
Two curves only?
A line and a curve?
Two lines?
Must be tangent to be called a cusp?
Should Legal Description wording be something like;
" to the point of cusp of a tangent curve..."?
" to the point of cusp with a tangent curve..."?
" to the point of cusp with a tangent line..."?
" to the point of cusp of a tangent line..."?
Or something else entirely?

[PLS7393]

You have the appropriate references, so no need for anyone's opinion.
My descriptions have used " . . . to a point of cusp; thence . . . "

As Wattles said when writing legal descriptions, "simplicity without ambiguity"

[Peter Ehlert]

Google has lots of definitions for "cusp", I started there and found confusion.

I believe the two references contradict a bit
Cuomo-Minnick demands that "both curves must have a common tangent"
Wattles does not require a "cusp" to have the same tangents, just "having the same general direction"

personally, I don't recall ever using the terms "cusp" or "point of cusp"... never saw the need to define it as such, but I have seen others use it

typically for complex curves I have used something like "...feet to the end of said curve; thence along a curve from which the radius point bears North 12°36'12" East, 800.00 feet distant, Westerly along said curve for an arc length of ..."
Simplicity in my mind

[PLS7393]

Wattles does not require a "cusp" to have the same tangents, just "having the same general direction"

Peter, if you look at Wattles, the "Point of Cusp" is tangent, and a point of cusp is only at that point of tangency with a curve.
I do not see any contradiction as you stated.

[Jim Frame]

I avoid the word entirely, preferring "to a point of reverse curvature" or "to a point of compound curvature," with appropriate defining criteria.

[Scott]

Thank you for the responses.

Wattles does not specifically state that the two entities must be tangent (although the diagram shows tangency) and also shows a cusp made up of a curve and a line.

Cuomo-Minnick (with contributions by Micheal J. Pallamary) explicitly states that it is not a cusp unless the two entities are tangent and implies a cusp is only between two curves.

I am seeking opinions for the apparent discrepancies stated above.

I am also seeking how the Surveying Community interprets “cusp” and the specific wording being actually used for scrivening a cusp in relation to the previous and next course in a description.

My opinion is that a cusp has to have at least one curve (cannot be composed of two lines) and the entities do not have to have a common radial bearing.

The wording I use is: ..."to a point of cusp with a (tangent or non-tangent) (curve or line) to which a radial bears Xxxxx ##°##'##" Xxxx..."

Another question I just thought of: Can the two entities of a cusp be called "tangent" to each other if there is a common radial bearing?

[pls5528]

Speaking of Cusp, this is most likely the most difficult of all areas in the state to perform a boundary retracement? San Antonio Heights, where "CUSPS" are the name of the game. The County Surveyor informed me that the engineer responsible for this map, ended up in an insane asylum. Most likely caused by trying to survey it?

[mpallamary]

I believe the correct way to use the term is whenever you have two curves intersecting at an odd configuration, where the curves do not meet at a logical place. A good example is if two curves meet, yet are non-tangent.

[mpallamary]

The San Antonio Map is quite beautiful!

[pls5528]

This one is on my office wall to remind me of the one boundary (in my 46 years) I could NOT resolve with confidence. It was quite common to see monuments (record or not) at the intersections in disagreement by 10-20 feet. One of the monuments may have fit a block well, but not the others. I am of the understanding that the San Bernardino County Surveyor stepped in and filed a map to resolve some of the issues.

[mpallamary]

Have you ever seen the map of La Jolla? Some of the most valuable land in Southern California.

[PLS7393]

I avoid the word entirely, preferring "to a point of reverse curvature" or "to a point of compound curvature," with appropriate defining criteria.

Jim, a "Point of Cusp" is not a point of compound curvature, or point of reverse curve. By definition and shown in Wattles diagram, a point of cusp is the point of tangency with a line or reverse curve.

[mpallamary]

http://mathworld.wolfram.com/Cusp.html

https://en.wikipedia.org/wiki/Cusp_(singularity)

[Dave Lindell]

Cusps are like pornography.
I know one when I see one.

[land butcher]

Quite a map. Downtown Hawthorne, CA was similar to that. Most was removed in the 70s for a mall that was vacated 20 years later.

[land butcher]

Cusps are like pornography.
I know one when I see one.

LOL but true.

[Anthony Maffia]

I read "point of cusp" to be the BC of a curve that comes back from the direction the previous course came from, either a line or curve, tangent or non-tangent, as opposed to at tangent/non-tangent curve to the left//right, which continues along the same path of travel as the prior curve/line.

Example from CalTrans (not in inclusive of uses of the term):

CALLS TO A NON-TANGENT CURVE': A "to" call is added to the description of the preceding straight line call as follows " ... to a point of cusp with a non tangent curve, concave [ direction], having a radius of [distance] feet, the initial radial of which bears [bearing];"

The course along the curve is then described as above.

http://www.dot.ca.gov/hq/row/landsurvey ... amples.pdf

I love the old maps. We have similar maps up north, which often can only be interpreted by a split of curbs for the block.