Curve of intersection of two surfaces calculator

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# Curve of intersection of two surfaces calculator

The most common way is to use the intersection classes derived from OdGeEntity3d:. Another way is to use the intersectWith methods that are available for some curves and surfaces. See the API reference online login required for the list of all methods and their usage. Intersection classes require two input entities that can be set in a constructor or by using a set method. Intersection classes do not own their base curves and surfaces. For curve intersections, you can optionally specify the range of curves to find intersections within; in this case the domain of curves is ignored.

All intersections are calculated automatically on the first call of one of the query functions, e. Using the set method invalidates all previously calculated intersections. Each intersection has its own index.

Note that points and curves have an independent numeration for curve intersectors, i. Ends of the overlapping intersections are not returned as separate intersection points. Intersection curves can touch each other at the ends. These functions return NULL if they are called twice for the same intersection. For the most common intersections, there are intersectWith methods. For curve-curve or curve-surface intersections, intersectWith returns true if this entity and the parameter entity have at least one intersection point intersection curves are ignored. The number of intersections is received in the parameter numInt.

Intersection points are received in the parameters p, p1, p2, p3, and p4. Note that the intersectWith methods for linear entities retrieve an intersection point even if it lies on the continuation of entities and the returned value is false.

For surface-surface intersections, intersectWith returns true if this entity and the parameter entity have an intersection curve, which is received in the parameter intLine. May 21, Tags: Intersections.

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Work with Intersection Classes Intersection classes require two input entities that can be set in a constructor or by using a set method. There are two types of intersections: Intersection points Intersection curves Each intersection has its own index.

Examples: 1. OdGeLineSeg3d line; if plane1.In geometryan intersection curve is, in the most simple case, the intersection line of two non-parallel planes in Euclidean 3-space. In general, an intersection curve consists of the common points of two transversally intersecting surfacesmeaning that at any common point the surface normals are not parallel.

This restriction excludes cases where the surfaces are touching or have surface parts in common. The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a the intersection of two planes, b plane section of a quadric sphere, cylinder, cone, etc.

## How do I find the points of intersection between two curves?

For the general case, literature provides algorithms, in order to calculate points of the intersection curve of two surfaces. In any case, the intersection curve of a plane and a quadric sphere, cylinder, cone, For details, see.

In any case parallel or central projectionthe contour lines of quadrics are conic sections. See below and Umrisskonstruktion. It is an easy task to determine the intersection points of a line with a quadric i.

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So, any intersection curve of a cone or a cylinder they are generated by lines with a quadric consists of intersection points of lines and the quadric see pictures. In general, there are no special features to exploit. One possibility to determine a polygon of points of the intersection curve of two surfaces is the marching method see section References.

It consists of two essential parts:.

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For details of the marching algorithm, see. The marching method produces for any starting point a polygon on the intersection curve. If the intersection curve consists of two parts, the algorithm has to be performed using a second convenient starting point. The algorithm is rather robust. Hence the contour line of a quadric is always a plane section i. The intersection curve of two polyhedrons is a polygon see intersection of three houses. The display of a parametrically defined surface is usually done by mapping a rectangular net into 3-space.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Hint : Think about trigonometric identities. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Parametrize the curve of intersection of 2 surfaces Ask Question. Asked 7 years ago. Active 7 years ago. Viewed 61k times. Thank you. Amzoti Steven Steven 43 1 1 gold badge 1 1 silver badge 4 4 bronze badges.

Vector function for the curve of intersection of two surfaces (KristaKingMath)

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Featured on Meta. Feedback post: New moderator reinstatement and appeal process revisions. The new moderator agreement is now live for moderators to accept across the…. Linked 3. Hot Network Questions. Question feed.You can use intersection curves to measure the thickness of a cross section of a part.

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All rights reserved. Intersection Curves Intersection Curve opens a sketch and creates a sketched curve at the following kinds of intersections: A plane and a surface or a model face. Two surfaces. A surface and a model face. A plane and the entire part. A surface and the entire part. You can use the resulting sketched intersection curve in the same way that you use any sketched curve, including the following tasks: Measure thickness at various cross sections of a part.

Create sweep paths that represent the intersection of a plane and the part. Make sections out of imported solids to create parametric parts. To use the sketched curve to extrude a feature, the sketch that opens must be a 2D sketch. Other tasks can be performed using a 3D sketch.

To open a 2D sketch, select the plane first then click Intersection Curve. To open a 3D sketch, click Intersection Curve first then select the plane. Parent topic Sketch Tools. To measure the thickness of a cross section of a part:. A 3D sketch opens because you clicked before selecting a plane. A sketched spline appears at the intersection of the plane and the top face.Post all your math-learning resources here. Questions, no matter how basic, will be answered to the best ability of the online subscribers. Follow reddiquette. Be civil and polite; this is meant to be an approachable community for discussion of reason and logic.

### How do I plot the line of intersection between two surfaces?

What does your instructor or the text want you to accomplish? Where are you in the process? Provide those who help with as much information as possible. Do I just set them equal to each other i. What if I am wondering about the intersection between a plane and a sphere? This is also something to do with intersection between two surfaces isn't it? Also what would just solving the system of linear equations give assuming that Aand B are just planes.

I can draw it in 3D if you'd like to help you understand. I guess in this problem the normal vector to the level surface and level curve is the same? Do you know how they managed to do that?

The first sketch is the projection to the xy plane and the second to the yz. There's some examples in there also. So from what I understand you are trying to do is find the Equation of the line that intersects the planes. Cross multiply your normals a X b to get the line L.

This line is parrallel to the the line of intersection. Now add this point to the line L and you will have your equation of the line that intersects both planes as a parametric equation.

What do you mean "two surfaces that are not planes"? The equations you gave are planes. Source Why? Creator ignoreme deletthis. Use of this site constitutes acceptance of our User Agreement and Privacy Policy.

All rights reserved. Want to join? Log in or sign up in seconds. Get an ad-free experience with special benefits, and directly support Reddit. Here, the only stupid question is the one you don't ask.But in this case we can use another method, which may be more useful: giving the coordinates of the points on the curve by expressions in some common variable called a "parameter" which may or may not be one of the coordinates. Roughly, what we expect is that a single equation in three variables determines a surface in space; two equations determine a curve or curves in the sense that the common solutions x,y of both equations form one or more curves ; and three dermine a point or isolated points.

And if we consider the infinitely many planes that all pass through the same line, then any two or more of their corresponding linear equations will still determine that common line. But "each new equation cuts down the dimension by one" is a handy rule of thumb.

The real question is the more basic one: Is it true that the gradient is always perpendicular to the contour at its base? Here is a piece of the original surface, with -2,2,-1 at one corner and with the above gradient vector drawn in dark green.

The reader is invited to download the corresponding Winplot file and rotate it to see that gradient is indeed perpendicular to the surface. Let us suppose that we want to find all the points on this surface at which a vector normal to the surface is parallel to the yz -plane. It is not clear, at least to me, that there are any such points; as I picture vectors perpendicular to the surface, they all seem to go forward or backward, at least slightly.

But let us see what calculus tells us. So the desired points are on both the original surface and the new surface determined by this new equation shown in blue to the right.

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Those points are arranged in two curves, drawn in green in this diagram.When two three-dimensional surfaces intersect each other, the intersection is a curve. We can find the vector equation of that intersection curve using these steps:. I create online courses to help you rock your math class. Read more. Set the curves equal to each other and solve for one of the remaining variables in terms of the other. Define each of the variables in terms of the parameter??? Generate the vector function that describes the intersection curve using the formulas. Find the vector function for the curve of intersection of the surfaces. Since both of the curves have??? We want to define each variable in terms of the parameter???

To find??? Now we have parametric equations for the curve of intersection, defined by. With the parametric equations in hand, we can plug each of them into the formula for the vector function.

This is the vector function for the curve of intersection. You can also write it as. Finding the vector function for the curve of intersection of two surfaces. The intersection of two surfaces will be a curve, and we can find the vector equation of that curve When two three-dimensional surfaces intersect each other, the intersection is a curve. I'm krista. Set the curves equal to each other and solve for one of the remaining variables in terms of the other Define each of the variables in terms of the parameter???

Generate the vector function that describes the intersection curve using the formulas??? Process for finding the vector function that gives the curve of intersection of two surfaces. Take the course Want to learn more about Calculus 3? I have a step-by-step course for that. Learn More. Vector function for the curve of intersection of an ellipsoid and a plane Example Find the vector function for the curve of intersection of the surfaces.

The ellipsoid??? The plane??? 