I create online courses to help you rock your math class. The trend of the pole is opposite the direction a plane dips. The parametric equation of the line is simple to obtain once the vector equation is known. The intersection of two planes university of waterloo. This is a curved line inside a circle that represents the line of intersection of a plane and the inside of a lower hemisphere, like the inside of a bowl. Strike dip 030 30 057 33 043 33 078 40 092 53 100 59 107 70 011 32 335 43 325 55 315 63 311 73 2. No other part of the spherical triangle represents a line of steeper dip than. This brings together a number of things weve learned. If we repeat this operation for all the points of intersection of the plane with the hemisphere then a curved line, a great circle trace, is formed on the streonet. I havent really worked with mathematica that much, and therefore i dont know how i should get these answers, and also plot the intersection of these two planes. Once it is found, rotate the tracing paper until the intersection is aligned with either the northsouth or eastwest vertical great circle fig. Stereonet clip 6 intersection of two planes duration. The intersection of two planes forms a line in 3dimensional space which plots as a point on the stereonet. We saw earlier that two planes were parallel or the same if and.
To illustrate, we will find the true dip and strike of a plane for which we have measured two apparent dips. Stereographic projection the basics geological digressions. Although some planes lines of intersection may be dipping at angles greater than the friction angle, sliding is not. Focal mechanism solutions utilize stereonet representations of fault plane orientations. However, not all lines of maximum dip on a stereonet projection will be candidates for the sliding direction. Once you have a point of intersection common to the 2 planes, the line just goes. The stereographic projection relates to the plane inversion in a simple way. Apply construction 62 twice for two different cutting planes to find two intersection points, x and y. Since the intersection of two planes forms a line, we will plot the hinge as a dot on the stereonet. How to use a paper stereonet to find the line of intersection between two planes. If the line l is a finite segment from p 0 to p 1, then one just has to check that to verify that there is an intersection between the segment and the plane.
Count in from the outer circumference to find the plunge. The three structural discontinuity sets, represented by the great circles plotted in figure 1. These threedimensional features are commonly represented on a twodimensional projection called a stereonet. Finding the trend and plunge of the intersection of two planes. The orientation is converted automatically to a line with a trend and plunge, but still remains veiwable as a rake. Gr tu4stereonet civl2002 engineering geology and rock. May 27, 2005 how do i find the line of intersection of two planes.
A wedge failure may occur when the line of intersection of two discontinuities, forming the wedgeshaped block, plunges in the same direction as the slope face and the plunge angle is less than the slope angle but greater than the friction angle along the planes of failure. Similar to planar failures, seve ral conditions relating to the line of intersection must be met for wedge failure to be kinematically admissible. Contents school of earth and environment 14 lineations due to intersection of two planes where two planes intersect a lineation is created on one plane where the other plane cuts through it. For the second menu, entries are added to a planes dataset plotted as great circles. Lecture notes mineralogy stereographic projections. B geologic methods for describing lines and planes c attitude symbols for geologic maps d reference frames ii definitions of points, lines, and planes a point 1 defined by one set of coordinates an ordered triple in 3d 2 defined by distance and direction from a reference point 3 intersection of two lines 4 intersection of three planes b line. Flatlying bedding contacts cropping out on sloped topography. Crains petrophysical handbook structural analysis stereonets. Grtu4stereonet civl2002 engineering geology and rock. The trend and plunge of this line can be read directly off the stereonet. A geological structures are represented by one or more lines or planes. Since the line is common to both planes, its direction vector can be used as a direction vector in each plane. We can use the intersection point of the line of intersection of two planes with any.
A great circle is the line of intersection with the surface of a sphere of a plane that passes through the center of the sphere. In general, two planes are coincident if the equation of one can be. Mar 20, 2019 the green represents the planes orientation when north is rotated back to its standard topofthe stereonet position. We collected a bunch of planar data from the limbs of a fold. In order to explicitly find it, you need a point on the line and the direction of it. It projects as a point in the middle of the stereonet. Find the parametric equations for the line of intersection of the planes. Map patterns and finding the strike and dip from a mapped. To record the dip of a plane all that is needed are two numbers. Jul 30, 2015 jr plots two planes and finds the orientation of their intersection line. Finding the line of intersection of two planes is simple. Any system of equations in which some variables are each dependent on one or more of the other remaining variables.
Spherical projections with osxstereonet sciencedirect. The intersection of the great circles defines the fold axis. The floor and a wall of a room are intersecting planes, and where the floor meets the wall is the line of intersection of the two planes. So this cross product will give a direction vector for the line of intersection.
When two planes intersect they define a line, which is common to both planes. Orientations of lines and planes in space a definitions of. If a plane projects onto the stereonet as a great circle, then a line or lineation on the plane will plot as a point on the same great circle. B a line can be defined in threedimensional space by its angle with three orthogonal axes. Parametric equations for the intersection of planes. Find both the vector equation and the parametric equation of the line containing the points p 1,2. In the above diagram two planes are plotted, one red, one blue. In 3d, two planes p 1 and p 2 are either parallel or they intersect in a single straight line l. Rotate the tracing paper until the intersection of the two planes lies on the eastwest diameter of the stereonet. A vertical plane will produce a straight line that passes through the. The plunge of a pole and the dip of a plane sum to 90. For question 2,see solved example 5 for question 3, see solved example 4 for question 4,put the value of x,y,z in the equation of plane. Two planes are coincident when they are the same plane.
Strikes and azimuths bearings are read around the primitive of the stereonet, dips and plunges are read along the equator. The intersection line between two planes passes throught the points 1,0,2 and 1,2,3 we also know that the point 2,4,5is located on the plane,find the equation of the given plan and the equation of another plane with a tilted by 60 degree to the given plane and has the same intersection line given for the first plane. The pole to a plane is a line that is perpendicular to the plane. Given two planes in two adjacent views, where the planes are defined by. Lineations due to intersection of two planes where two planes intersect a lineation is created on one plane where the other plane cuts through it. Important tips for practice problem for question 1,direction number of required line is given by1,2,1,since two parallel lines has same direction numbers. The stereonet itself shows the projection of great circles and small circles. Mark the outer circle at the closest end of the ns or ew line. Determining the orientation of a line of intersection between two planes a.
To find the direction, you determine the cross product of the two normals of the two planes since the line must be perpendicular to both normals. The orientation of a plane is represented by imagining the plane to pass through the centre of a sphere fig. As long as the planes are not parallel, they should intersect in a line. Intersections are used in kinematic analysis for wedge sliding and direct toppling failure modes, and can also be contoured like pole or dip vectors. Figure 10 shows a beddingcleavage lineation where cleavage cuts bedding and a joint cleavage lineation where cleavage cuts the joint surface. The idea is similar in its goal to representing the threedimensional surface of the earth in two dimensions on a topographic map. The stereonet grid is divided into two degree segments with a thicker ten degree lines figure 4.
Lecture 1s finding the line of intersection of two planes page 55 now suppose we were looking at two planes p 1 and p 2, with normal vectors n 1 and n 2. If planes are parallel, their coefficients of coordinates x, y and z are proportional, that is. Plane dip and strike, lineation plunge and trend, structural measurment conventions, the brunton compass, field book, and njgs fms. Find the intersection of the line through the points 1, 3, 0 and 1, 2, 4 with the plane through the points 0, 0, 0, 1, 1, 0 and 0, 1, 1. Map patterns and finding the strike and dip from a. Lecture 1s finding the line of intersection of two planes. Find an equation of the plane passes through a point and has. Stereonets are commonly reported to be the leastintuitive part of structural geology.
Plane dip and strike, lineation plunge and trend, structural. Intersection of two planes in 3d, two planes will intersect in a line. A wedge failure may occur when the line of intersection of two discontinuities, forming the wedgeshaped block, plunges in the same direction as the slope face and the plunge angle is less than the slope angle but greater than the friction angle along the planes of failure hoek and bray, 1981 figure 1. Within a dipping plane the line at right angles to the strike line is the line with the steepest plunge. The point where the two great circles intersect defines the line contained by both planes. Equal angle stereonet pdf equal area stereonet with small circles showing consistent size. Stereonet practice problems do them first, then check solution on p. They are used for analysis of various field data such as bedding attitudes, planes, hinge lines and numerous other structures. Lecture 1s finding the line of intersection of two planes page 55 now suppose we were looking at two planes p. Plot the planes collected from the fold and the corresponding poles. The intersection of the two planes is the line x 2t 16, y t this system of equations was dependent on one of the variables we chose z in our solution.
Where p is the point of intersection, t can go from inf, inf, and d is the direction vector that is the cross product of the normals of the two original planes. Two planes are either parallel or they intersect in a line. The line is contained in the plane in nite intersections the line is parallel to the plane no intersections the line intersects the plane one point of intersection intersections of lines and planes. Structural geology laboratory university of south alabama. Two nonparallel planes i, ii meet in a line l not parallel to plane iii. Let p and q be two points on the sphere with projections p. Since any two planar surfaces intersect in a line, most rocks folded with concomitant development of an axial plane foliation display the between bedding and the axial plane. Besides, the intersection of two planes will not a point, but nothing, a line or a plane. To create the rst plane, construct a vector from the known. The line of intersection between the plane and the sphere will then represent a circle, and this circle is formally known as a. In three dimensions which we are implicitly working with here, what is the intersection of two planes. Intersecting planes when two planes intersect they define a line, which is common to both planes. For a positive ray, there is an intersection with the plane when.
I would appreciate it if someone could guide me or show me some way to do it. The procedures here are slightly simplified because we assume that planes are specified by right hand rule, our preferred convention. The line of intersection between the red and blue planes looks like this. A plane can be represented by its normal, which itself is a line. When planes intersect, the place where they cross forms a line. If two planes intersect each other, the intersection will always be a line.
Line of intersection of two planes middle right, above, shows how to find the angle between the two planes in the previous example. Rotate tracing paper so point of intersection lies on eastwest line of stereonet 1 make tick mark on primitive circle showing direction of. He calls multiple parks in the area that offer rock climbing and collects data on the height of the rock formations and the average time it takes people to reach the top and come back down. The subject of linear algebra includes the solution of linear equations. Garvinintersections of two planes slide 714 intersections of lines and planes intersections of two planes example represent the line r 3. The angle of dip is an angle between 0 for horizontal planes and 90 for vertical planes. I have an idea, but both of the planes have a 2z ie. I can see that both planes will have points for which x 0.
The line of intersection of two planes, projection of a. So, is there some other way to solve this, or am i missing something. In both a and b the intersection of the ruled plane with the structural plane defines a line true dip or apparent dip line that combined with the strike line. Def, find the intersection line by the twoview method. Plotting the orientation of a line the simplest geometric information one can display on a stereonet is the orientation of a vertical line. Line these two points up with a greatcircle and draw in the axial plane. We need to find the vector equation of the line of. Measure the plunge of the line of intersection and add an arrow pointing in the.
Rakes the stereonet program supports rakes through the input of a plane and an orientation rake in that plane. A small circle marks the path in space of a point on the surface of a sphere that is rotating about an axis. Understanding that the axial hinge is the point of maximum curvature or bending in a fold, it is going to be located at the intersection of the two limbs or great circles in this case. The trace of bedding on an intersecting foliation plane commonly appears as. Draw a great circle projection for each plane 1 there will be one unit point of intersection between the two great circles b. Stereographic projection is about representing planar and linear features in a two dimensional diagram. The line of intersection of two planes, projection of a line. Equation for the line of intersection between two planes. Rotate the tracing paper so that the point of intersection lies on the ns or ew line of the net. Jul 25, 2017 how to use a paper stereonet to find the line of intersection between two planes. We saw earlier that two planes were parallel or the same if and only if their normal vectors were scalar multiples of each other. To write the equation of a line of intersection of two planes we still need any point of that line.
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