# Intersect Matlab

Use the backslash when possible. Solving for y in terms of x in the line and substituting that back into the equation of the first ellipse gives you a quadratic equation in x which has two solutions, namely the x values of the two intersections of the two ellipses. If they do, there's no way the lines have a point of intersection. Proceedings of CVPR 2008, Anchorage, Alaska, June 2008. You can integrate STK and MATLAB to automate, extend or visualize your analysis. intersection of multiple arrays. Matlab obtaining intersection problem? I have two curves which are in the form of data, I need to find the intersection of the curves, in other words, the closest two points of them. INTERSECTION BETWEEN 2 IMAGES. We have one input value and two output values to transform a given number in both Celsius and Farenheit degrees Ex. As far s a circle goes, as Walter points out, surely you can compute the radius of a circle given the center and one point on the circumference. CameraPosition [x, y, z] Axes coordinates. The following is a SQL INTERSECT operator example that has one field with the same data type: SELECT supplier_id FROM suppliers INTERSECT SELECT supplier_id FROM orders; In this SQL INTERSECT example, if a supplier_id appeared in both the suppliers and orders table, it would appear in your result set. More than 40 million people use GitHub to discover, fork, and contribute to over 100 million projects. Get the free "Intersection points of two curves/lines" widget for your website, blog, Wordpress, Blogger, or iGoogle. *A2A* I am not a Matlab expert, so there may be a better way to do this. If that distance is larger than the radius of the sphere then there is no intersection. : Matrix manipulation. First we can test if the ray intersects the plane in which lies the disk. I already sought help and they explained that I should use 'find' and then the '==' to find where the output match. This will allow for further solutions for more complex questions, including a general solution regarding whether a point is inside or outside of a convex or non-convex polygon. We can run the code in the MATLAB Profiler to find out which operations are included in the consumed time. In the remainder of this blog post I'll explain what the Intersection over Union evaluation metric is and why we use it. Neglecting the effect of unknown correlations can result in grave consequence of performance deterioration, and even divergence. First, these two circles are on the same plane and they have two intersection points. Intersection of plane and line. An example of how to find the intersection of two linear equations using the find function. MATLAB - Vector Dot Product - Dot product of two vectors a = (a1, a2, â ¦, an) and b = (b1, b2, â ¦, bn) is given by −. Finding intersection of two sets in MATLAB is one of the most frequently used function if you are doing lots of data merging tasks. Note that the elements of union and intersection can be printed in any order. However, because this is a pair of quadratic equations, there are 4 possible solutions due to the sign ambiguity (i. intersection and provides at least one point on any connected intersection segment and identifies all singularities. After you import data into the MATLAB ® workspace, it is a good idea to plot the data so that you can explore its features. Planes through a sphere. Intersection of two planes. Plotting Data Introduction. How to create a 3D Terrain with Google Maps and height maps in Photoshop - 3D Map Generator Terrain - Duration: 20:32. [lat,lon] = gcxgc(lat1,lon1,az1,lat2,lon2,az2) returns in lat and lon the locations where pairs of great circles intersect. Show the intersection of two curves. Use the backslash when possible. The shapeID elements identify whether the corresponding vertex in polyout originated in poly1 , poly2 , or was created from the intersection. The Latest matlab full version is perfect tool of all time. We also offer training for non-members on a fee-for-service basis. These xls files alwasys have four cloummns but different number of rows, each colummn from left to right is considered as a, b,c and d. However, because this is a pair of quadratic equations, there are 4 possible solutions due to the sign ambiguity (i. MATLAB is designed to operate primarily on whole matr. If they do, there's no way the lines have a point of intersection. Intersection kernel is particularly useful for histograms and has been shown to be efficient in computer vision tasks. Is it possible to determine if the circle intersects with the polyhedron in MATLAB and if yes, how can I determine the polygon formed by the intersection of a 3d circle with a polyhedral shape? Please I will be glad if the computational geometry is also added but more emphsasis on the MATLAB programming. Let us now use the equation of the plane in Example 1 to find the point of intersection of the plane with the line through (1,2,-1) and. numel works with the overloaded subsref and subsasgn functions. I'm trying to use an if statement to plot a balls entire trajectory if it goes through a hole in the wall, and to plot the trajectory only up to the wall if it doesn't go through the hole. Using the arrow keys in a graph activates a free-moving trace. fieldname generates a comma-separated list. And also, what must I do if I have to determine the point of intersection for more than two lines using Matlab? Thanks. : Matrix manipulation. Using intersect() the operation took 58 seconds. Please find below the various list of operators. However, using a free-moving trace rarely locates the point of intersection of two graphs but instead gives you an approximation of that point. Learn more about matlab, set difference, intersection MATLAB. Learn more about intersection. area is then a matrix giving the intersection of all rectangles specified by A with all the. The functions also determine intersections of arbitrary vector data. Pre-covariance intersection. INTERSECTION BETWEEN 2 IMAGES. This can be done by clicking "Run and Time" button in the MATLAB Code Editor. The intersect function only supports this syntax when poly1 and poly2 are scalar polyshape objects. Use the backslash when possible. Berg and Jitendra Malik. I would like to know the point (x,y)where these lines intersect each other. In set theoretic terms, this is A B. Use MATLAB to determine the intersection point for the sets of equations shown below. The source code runs in 2-d, 3-d, 4-d, and higher dimensions. intersect(A & B): It is used to intersect A and B and returns the common values of A and B in sorted order. Gareth Rees describes the algorithm in a StackOverflow article on the subject. Union (∪) and Intersection (∩) symbols in LaTeX can be produced via the \cup and \cap definitions while in math mode. Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, furthest-site Delaunay triangulation, and furthest-site Voronoi diagram. A self intersection is a situation where a part of a surface mesh collides with another part of itself, i. You can try solving the equation f1(x,y,z) = f2(x,y,z) for y and z in terms of x either by hand or using the Symbolic Math Toolbox. We’ll use the ‘ fminsearch ’ function to find the intersection of the given curves or functions with several variables. MATLAB is designed to operate primarily on whole matr. Calculate intersection (overlapping area) of two polygons (of which one a 35 sided irregular polygon) without the use of polybool function. 0525 sin(Q*pi/180) = Q/900 - 0. Include a legend al 4x1+ 2x2 10 bl4x 2x2 10. The first question is whether the ray intersects the sphere or not. How can i find the intersection point between Learn more about image processing, digital image processing, interpolation, nonlinear, line. It is widely believed that the unknown correlations ubiquitously exist in a diverse range of multi-sensor fusion problems. If it is scattered data, you can use the interpolation functions for scattered data in MATLAB, "griddatan", which takes in scattered data and returns the value of the function at the query points. Intersection of two matrices. Is it possible to determine if the circle intersects with the polyhedron in MATLAB and if yes, how can I determine the polygon formed by the intersection of a 3d circle with a polyhedral shape? Please I will be glad if the computational geometry is also added but more emphsasis on the MATLAB programming. For RPP/RPP surface intersections a more convenient set of such points sufficient to discover all connected components of the intersection, includes border and collinear normal points between the two surfaces. Good luck in 2007! Sven Van Poucke, MD. If you've ever needed to find the intersections between (possibly complicated) curves, this file is for you. I'm trying to use an if statement to plot a balls entire trajectory if it goes through a hole in the wall, and to plot the trajectory only up to the wall if it doesn't go through the hole. A Macintosh PowerPC executable and MATLAB versions are also available. If VarsIn1 and VarsIn2 each contain Simulink. I am writing a matlab programm to import xls files from local and do some calculations. intersect(A & B): It is used to intersect A and B and returns the common values of A and B in sorted order. I want to extract intersection points for every litter and put it in a cell or whatever. How can I find and intersection values between Learn more about poly, polynomial, intersection MATLAB. Learn more about intersect. These codes compute overlap (intersection over union) of two circles, count number of true positives, false positives and false negatives as well as they compute recall, precision, F1-score and area-under-curve (AUC) using Matlab, Python and C++. Is there a function to find the intersection of two lines on a plot? I looked for something like this but only found a function that. The input for triangle T is given in the form of three points (its three vertices v0, v1 and v2). The last step you need to take is to transform it into numeric. Is it possible to determine if the circle intersects with the polyhedron in MATLAB and if yes, how can I determine the polygon formed by the intersection of a 3d circle with a polyhedral shape? Please I will be glad if the computational geometry is also added but more emphsasis on the MATLAB programming. c = intersect(A,B) returns the values common to both A and B. and you want to find any intersection points. However if you would like to do the same for many sets, there are not many alternati. Write a program in MATLAB to perform Union,Intersection and Complement operations. I welcome any comments, suggestions, bug reports etc. Meanwhile as required, I edit my question to make it more clear. Use the backslash when possible. Implicit Surface Intersections. There is no direct way to compute the line of intersection between two implicitly defined surfaces. I am writing a matlab programm to import xls files from local and do some calculations. HW5_4 Use MATLAB to determine the intersection point for the sets of equations shown below. I need to write a function (preferably with OUT a for loop, as length(A)=big) to give me the intersection of all the contents of A, so that here, f(A) = [1 2]; % this is the intersection of A{1} through A{3}. Neglecting the effect of unknown correlations can result in grave consequence of performance deterioration, and even divergence. , two mesh elements intersect each other. These xls files alwasys have four cloummns but different number of rows, each colummn from left to right is considered as a, b,c and d. C = intersect(A,B,vars). , whether the objects intersect at all, or location, where the actual intersection location where the two moving objects first hit is formed. mat file and the other on is: Th=. Plot the functions x^8 and 4^x on the same graph, and determine how many times their graphs intersect. Use MATLAB to determine the intersection point for the sets of equations shown below. Orange Box Ceo 7,004,597 views. I tried doing following and came up with the value of parameters 't' and 's', but I need help to find out the value coordinates of the intersection point by plugging in 't' and 's'. I'll also provide a Python implementation of Intersection over Union that you can use when evaluating your own custom object detectors. For example: Given set. You can download the script for this video here: https://github. intersect(A & B, ‘rows’): It returns rows common to both A and B. You can try solving the equation f1(x,y,z) = f2(x,y,z) for y and z in terms of x either by hand or using the Symbolic Math Toolbox. Plotting a circle and finding intersections. This example shows how to measure the angle and point of intersection between two beams using bwtraceboundary, which is a boundary tracing routine. intersection of multiple arrays. The meaning of those intersections is that the given lines or curves have the same coordinate values at some points. However, using a free-moving trace rarely locates the point of intersection of two graphs but instead gives you an approximation of that point. This can be done by clicking "Run and Time" button in the MATLAB Code Editor. As far s a circle goes, as Walter points out, surely you can compute the radius of a circle given the center and one point on the circumference. Lines, Planes and MATLAB. You can integrate STK and MATLAB to automate, extend or visualize your analysis. x1,y1 and x2,y2. Example: Discover what MATLAB. Intersections between two symbolic functions. Since (a,b) is on both graphs, the line and the curve, is satisfies both equations. Using intersect() the operation took 58 seconds. Intersection between a Line Segment and a Triangle. In the following discussion, the. Example: A custom-made Matlab function Even though Matlab has plenty of useful functions, in this example we develop a custom-made Matlab function. Meanwhile as required, I edit my question to make it more clear. The intersection point occurs where -0. Level up your coding skills and quickly land a job. I would like to know the point (x,y)where these lines intersect each other. You have to line segments and you want to know if they intersect. These xls files alwasys have four cloummns but different number of rows, each colummn from left to right is considered as a, b,c and d. Latest Matlab Crack is the software that any one need. You can use the TI-84 Plus calculator to find accurate points of intersection for two graphs. Why am I still getting n12=n1. c = intersect(A, B) returns the values common to both A and B. Solving for y in terms of x in the line and substituting that back into the equation of the first ellipse gives you a quadratic equation in x which has two solutions, namely the x values of the two intersections of the two ellipses. Because arrays operations are so similar to the equivalent mathematical operations, a basic knowledge of linear algebra is mandatory to use matlab. No loops are used throughout, taking full advantage of MATLAB's vectorization capabilities. Each circle with have either 0, 1, or 2 intersection points. It shall be assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice. Recently, there was an interesting question about them on MATLAB Answers. The controller is developed based on the. To find intersection point of two lines ?. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Planes through a sphere. A and B can also be matrices, where each row is a position vector. If VarsIn1 and VarsIn2 each contain Simulink. If the equations do not intersect, graph them anyway. Get the free "Intersection points of two curves/lines" widget for your website, blog, Wordpress, Blogger, or iGoogle. c = intersect(A,B) returns the values common to both A and B. The intersect function does not seem to work: intersect(n1,n2) ans = 1×0 empty double row vector The only way I can do it now is by zooming in the plot area and visually marking the intersection. intersection point between 2-d plot and a line. The functions also determine intersections of arbitrary vector data. (Hint: You will probably have to make several plots, using various intervals, in order to ﬁnd all the intersection points. Sometimes there will be no intersection at all. If A and B are tables or timetables, then setdiff returns the rows from A that are not in B. We talked about implicit surfaces here back in March. Recently, there was an interesting question about them on MATLAB Answers. In the following discussion, the. The equations apply to lines, if the intersection of line segments is required then it is only necessary to test if u a and u b lie between 0 and 1. Learn more about plane MATLAB. A and B can be cell arrays of strings. The intersect function only supports this syntax when poly1 and poly2 are scalar polyshape objects. stl" file (from whatever CAD program) within Matlab in terms of faces (f) and vertices (v). Example: A custom-made Matlab function Even though Matlab has plenty of useful functions, in this example we develop a custom-made Matlab function. To find union, intersection and complement of matrices using Matlab. This description is the same as intNormalizedDistance1To2 except that i and j are swapped in the description, and that doesn't really make any sense. Intersection of Two Parabolas. Plotting a circle and finding intersections. This paper describes a computational method for removing self intersections of a triangular mesh. In that case we say the answer is the "empty set" or the "null set". We will only discuss scripts here. c = intersect(A, B) returns the values common to both A and B. For example:. You can integrate STK and MATLAB to automate, extend or visualize your analysis. However, if you want to suppress and hide the MATLAB output for an expression, add a semicolon after the expression. (Hint: You will probably have to make several plots, using various intervals, in order to ﬁnd all the intersection points. MATLAB can plot a 1 x n vector versus an n x 1 vector, or a 1 x n vector versus a 2 x n matrix (you will generate two lines), as long as n is the same for both vectors. Normal Boundary Intersection. Here as you can see into attached figure, I need to find intersection points 1,2,3 and 4. If A and B each specify one rectangle, the output area is a scalar. The traffic signal controller for segregate intersection is shown in Figure 1 is designed based upon the normal traffic system for two-way single intersection. This will allow for further solutions for more complex questions, including a general solution regarding whether a point is inside or outside of a convex or non-convex polygon. A plane can intersect a sphere at one point in which case it is called a tangent plane. C = intersect(A,B,vars). However if you would like to do the same for many sets, there are not many alternati. Orange Box Ceo 7,004,597 views. For a positive ray, there is an intersection with the. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Please try again later. The plot command can also be used with just one input vector. The input for triangle T is given in the form of three points (its three vertices v0, v1 and v2). If the equations do not intersect, graph them anyway. The first question is whether the ray intersects the sphere or not. Advantages of STK-MATLAB Integration. Learn more about matlab, set difference, intersection MATLAB. The great circles are defined using great circle notation, which consists of a point on the great circle and the azimuth at that point along which the great circle proceeds. I really like the interface to. Currently I'm using this code but the fsolve command doesn't reach a conclusion, probably because I'm not choosing a good initial guess. Neglecting the effect of unknown correlations can result in grave consequence of performance deterioration, and even divergence. Roundabouts have certain distinguishing features and characteristics (as shown in the adjacent diagram). Graph the equations with different colors, and plot the intersection point with a red star marker. Pre-covariance intersection. Satisfaction of this condition is equivalent to the tetrahedron with vertices at two of the points on one line and two of the points on the other line being degenerate in the sense of having zero volume. 1 A graphical solution with fooplot. Vertical asymptotes almost always occur because the denominator of a fraction has gone to 0, but the top hasn't. VariableUsage objects in VarsIn1 with the same properties of the objects in VarsIn2. Learn more about intersection. ) Now ﬁnd the values of the points of intersection, ﬁrst using the fzero command and then using the solve command. Nan stands for 'not a number'. There are two types of M-files, scripts and functions. First, these two circles are on the same plane and they have two intersection points. INTERSECTION BETWEEN 2 IMAGES. We realised we could help companies working in a 2D world to bring all sorts of data into an XR space. Intersections between two symbolic functions. Modifications : The original package of LIBSVM 3. Plotting Data Introduction. 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. Constructs a sorted range beginning in the location pointed by result with the set intersection of the two sorted ranges [first1,last1) and [first2,last2). I am writing a matlab programm to import xls files from local and do some calculations. Why am I still getting n12=n1. Sometimes there will be no intersection at all. , whether the objects intersect at all, or location, where the actual intersection location where the two moving objects first hit is formed. intersection point between 2-d plot and a line. By Huide Zhou Université de Technologie de Belfort-Montbéliard E-mail: prettyage. Using intersect() the operation took 58 seconds. After you import data into the MATLAB ® workspace, it is a good idea to plot the data so that you can explore its features. View Lab Report - Matlab_assign from CSE 2076 at University Polytechnic BIT Mesra. However, I just realize I may post this on the wrong place. Intersections between two symbolic functions. Matlab R2015b full version do processes with more speed as compared to the older. An exploratory plot of your data enables you to identify discontinuities and potential outliers, as well as the regions of interest. It shall be assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice. For timetables, setdiff takes row times into account to determine equality, and sorts the output timetable C by row times. It is widely believed that the unknown correlations ubiquitously exist in a diverse range of multi-sensor fusion problems. " doc, help % for help with various matlab functions " whos % Lists all the variables in current workspace " clear % clears all variables in the current workspace. Asked by Chirag Bhuva. Faster postings list intersection via skip pointers In the remainder of this chapter, we will discuss extensions to postings list data structures and ways to increase the efficiency of using postings lists. In this published M-file, we will use MATLAB to solve problems about lines and planes in three-dimensional space. VariableUsage objects that have the same values for these three properties, they both describe the same variable. c = intersect(A, B) returns the values common to both A and B. Simply convert the result using double. *A2A* I am not a Matlab expert, so there may be a better way to do this. The idea is to choose one line, and see if the end points from the other line lie on the same side. intersect1d (ar1, ar2, assume_unique=False, return_indices=False) [source] ¶ Find the intersection of two arrays. The meaning of those intersections is that the given lines or curves have the same coordinate values at some points. c = intersect(A,B,'rows') when A and B are matrices with the same number of columns returns the rows common to both A and B. Solving we get: 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. Any point on that line is a. We've come to expect great things from Doug, and this file is no exception. Line 1 is made up of two points A and B and line 2 comprise of C and D. (Hint: You will probably have to make several plots, using various intervals, in order to ﬁnd all the intersection points. VariableUsage objects in VarsIn1 with the same properties of the objects in VarsIn2. MATLAB - Operators - An operator is a symbol that tells the compiler to perform specific mathematical or logical manipulations. When the circles do not intersect or are identical, NaNs are returned. If it is scattered data, you can use the interpolation functions for scattered data in MATLAB, "griddatan", which takes in scattered data and returns the value of the function at the query points. Products; So they will intersect in a line. Classification Using Intersection Kernel Support Vector Machines is efficient. My problem tells me to plot and then find and print the points of intersection for x=[2:7]. For a pairing of a great circle with a small circle, there are four possible intersection conditions: the circles are identical (possible because great circles are a subset of small circles), they do not intersect, they are tangent to each other (the small circle interior to the great circle) and hence they intersect once, or they intersect twice. Select a Web Site. The intersection of two sets is formed only by the elements that are present in both sets. However if you would like to do the same for many sets, there are not many alternati. Choose a web site to get translated content where available and see local events and offers. If not, the second line might intersect the first one, or the point of intersection may fall outside the limits of the first line segment. Back Function Institute Mathematics Contents Index Home. Long story short: if there's a way to get all zeros using matlab, I'm not aware of it. 0525 sin(Q*pi/180) = Q/900 - 0. numel works with the overloaded subsref and subsasgn functions. second, the radius, the centers and the normal vector are known. I welcome any comments, suggestions, bug reports etc. Level up your coding skills and quickly land a job. If that distance is larger than the radius of the sphere then there is no intersection. Recently, there was an interesting question about them on MATLAB Answers. A and B can be cell arrays of strings. How to find point of intersection between two lines, Intersection between two lines (java, javascript, c++, c#, python, matlab) In this tutorial, this is the line segment intersection algorithm. The following is a SQL INTERSECT operator example that has one field with the same data type: SELECT supplier_id FROM suppliers INTERSECT SELECT supplier_id FROM orders; In this SQL INTERSECT example, if a supplier_id appeared in both the suppliers and orders table, it would appear in your result set. We talked about implicit surfaces here back in March. If so, it will calculate the actual intersection point. We will cover a method for finding the point or points of intersection for two quadratic functions. 1453*ones(527,1); plot(Th). MATLAB programs are called M-files, and are saved with the extension. How do I check (in MATLAB) whether two finite line segments, L1 (drawn between points (x1,y1) and (x2,y2)) and L2 (drawn between points (x3,y3) and (x4,y4)), intersect with each other? Please note that intersection point is not needed, Only boolean answer (yes or no). And can I solve it with vectors (as answered by Jan)? I can take two normal vectors and get cross product vector (= direction of intersection line) and then get just some point of intersection to locate the line. Use the backslash when possible. So i can plot the lines using these point data sets. Graph the equations with different colors, and plot the intersection point with a red star marker. I welcome any comments, suggestions, bug reports etc. There are two types of M-files, scripts and functions. Therefore, we suggest that you copy the nyquist1. If VarsIn1 and VarsIn2 each contain Simulink. User Hg offered an image containing two intersecting curves. The location of the camera. Plot the functions x^8 and 4^x on the same graph, and determine how many times their graphs intersect. If A and B each specify one rectangle, the output area is a scalar. Whether you are an experienced MATLAB user or a novice, you may not be fully aware of MATLAB's graphing abilities. Currently I'm using this code but the fsolve command doesn't reach a conclusion, probably because I'm not choosing a good initial guess. Learn more about intersection. As a novice in matlab, I can not find the right approach. However, using a free-moving trace rarely locates the point of intersection of two graphs but instead gives you an approximation of that point. Toggle Main Navigation. Plotting Data Introduction. Asked by Chirag Bhuva. -----INTERX Intersection of. Learn more about plane, matrix, intersection, vector MATLAB. Note: The MATLAB nyquist command does not provide an adequate representation for systems that have open-loop poles on the imaginary axis. This MATLAB function returns the intersection points of two polylines in a planar, Cartesian system, with vertices defined by x1, y1, x2 and y2. Define this routine as a string that is a valid MATLAB expression or the name of an M-file. Graph the equations with different colors, and plot the intersection point with a red star marker. Learn more about circle, intersect, grid, plot. MATLAB - Vector Dot Product - Dot product of two vectors a = (a1, a2, â ¦, an) and b = (b1, b2, â ¦, bn) is given by −. While a few other functions already exist in FEX that compute the intersection points of curves, this short piece of code was written with speed being the highest priority. MATLAB - Vector Dot Product - Dot product of two vectors a = (a1, a2, â ¦, an) and b = (b1, b2, â ¦, bn) is given by −. If these two lines intersect, then sometimes it might be important to find the coordinates of this intersection. We talked about implicit surfaces here back in March. To find the intersection point is to find the point x such that y1(x)=y2(x). I already sought help and they explained that I should use 'find' and then the '==' to find where the output match. [lat,lon] = gcxgc(lat1,lon1,az1,lat2,lon2,az2) returns in lat and lon the locations where pairs of great circles intersect. PDF | This paper presents a MATLAB simulation of fuzzy traffic controller for controlling traffic flow at multilane isolated signalized intersection. We can run the code in the MATLAB Profiler to find out which operations are included in the consumed time. : Matrix manipulation. Because arrays operations are so similar to the equivalent mathematical operations, a basic knowledge of linear algebra is mandatory to use matlab. For example:. Matlab R2015b full version do processes with more speed as compared to the older. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to $585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over $1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: