Defined coordinate system. Coordinate systems that are used in geodesy and topography

Programming in absolute coordinates G90. Programming in reference coordinates is G91. Instruction G90 interprets displacements as absolute values in relation to the active zero point. Instruction G91 interprets movements as an increase from previously reached positions. These instructions are modal.

Set the G92 coordinate value. The G92 instruction can be used in a block without axis (coordinate) information or with axis coordinate information. Due to the absence of axis information, all coordinate values are converted to the coordinate system of the verstat; In this case, all compensations (corrections) and zero reduction are cancelled. Due to the availability of axis information, the entered coordinate values are accurate. This instruction does not affect any movements occurring between one frame.

N…G92 X0 Y0 /The precise values of the X and Y coordinates are set to zero. More precisely, the Z coordinate value becomes permanent.

N…G92 / Corrections and zero reduction are considered.

Vibration of area – G17 (XY area), G18 (XZ area), G19 (YZ area). The instructions indicate the selection of the working plane from the coordinate system of the part and program. Work with instructions G02, G03, G05, programming in polar coordinates, equidistant correction without any choice.

Rukh trajectories (types of interpolation)

Linear interpolation transfers the motion of a straight line in a three-coordinate space. Before the start of interpolation procedures, the CNC system calculates the balance of the numbers resulting from the programming of the coordinates. The flow control process controls the contour feed so that its value is kept within acceptable values. The crash in all coordinates may end within one hour.

With circular interpolation, the flow moves along the specified working area. The parameters of the stake (for example, the coordinates of the end point and the center) are assigned to the head of the wheel, resulting from the programming of the coordinates. The flow control process controls the contour feed so that its value is kept within acceptable values. The crash in all coordinates may end within one hour.

Guent interpolation is a combination of circular and linear.

Linear interpolation with accelerated movement – G00, G200. In the rapid movement process, the programmed movement is interpolated, and the end point swing moves in a straight line with maximum feed speed. Fluidity and rapid feed, using the same axes, are maximum. The feed speed of other axes is controlled in such a way that the rotation of all axes ends at the end point at the same time. While instruction G00 is active, px is increased to zero in the skin frame. Since there is no need to increase the feed speed to zero in the skin frame, replace G00 with G200. The values of the maximum feed speed cannot be programmed, but rather set by so-called machine parameters in the memory of the CNC system. Instructions G00, G200 are modal.

Linear interpolation from programmed feed speed – G01. Movements from the specified feed speed (F words) straight to the end point of the frame proceed along a straight line. All coordinate axes complete rotation simultaneously. The feed speed of the end of the frame is reduced to zero. The contour feed speed is programmed, then. The feed values for the skin-rimmed coordinate axis will be smaller. The feed speed values should be determined by adjusting the “machine parameters”. Option for combining the words with the G01 instruction in the frame: G01_X_Y_Z_F_.

Circular interpolation – G02, G03. Movements in the frame occur according to the contour fluidity specified by the active F-word. The movement along all coordinate axes is completed in the frame at the same time. These instructions are modal. Feed drives specify movements along the stake using a programmed feed at the selected interpolation plane; In this case, instruction G02 indicates the direction behind the year arrow, and instruction G03 is opposite the year arrow. When programming the color, set the additional radius or coordinates to the center. An additional option for programming the stake is indicated by instruction G05: circular interpolation with access to a trajectory that is precise.

Programmed stake for additional radius. The radius must first be specified in the reference coordinates; on the basis of the end point of the arc, which can be specified in both relative and absolute coordinates. Based on the position of the cob and end points, as well as the radius value, the CNC system first determines the coordinates of the stake. The result of the expansion can be the coordinates of two points ML, MR, rotated in a similar way to the left and right hand in a straight line that connects the end and end points.

Rotating the center of the stake to lie under the sign of the radius; with a positive radius, the center is turned to the left, and for a negative radius - to the right. Removal of the center is also indicated by instructions G02 and G03.

Option for combining the text with the G03 instruction in the frame: N_G17_G03_X_Y_R±_F_S_M. Here: instruction G17 means selecting circular interpolation for the X/Y plane; Instruction G03 means circular interpolation directly opposite the year arrow; X_Y_ are the coordinates of the end point of the stake arc; R – radius of the stake.

Programming the stake for additional coordinates to the center. The coordinate axes for which the position of the center is determined are parallel to the axes X, Y and Z, and the coordinates associated with the center are called I, J and K. The coordinates are set between the starting point of the arc of the stake. її center M on straight lines parallel to the axes. The sign is indicated directly from the vector A to M.

N… G90 G17 G02 X350 Y250 I200 J-50 F… S… M…

The butt of the double stake is programmed: N... G17 G02 I... F... S... M...

Circular interpolation with access to a circular path is scrupulous – G05. The CNC system uses instruction G05 for the expansion of such a circular plot, exiting from the front frame (with linear or circular interpolation) in decimal places. The parameters of the arc that is being formed are calculated automatically; tobto. The end point is programmed, but the radius is not specified.

Gwent interpolation - G202, G203. Helical interpolation consists of circular interpolation for the selected area and linear interpolation for other coordinate axes, up to six circular axes. The circular interpolation area is specified using instructions G17, G18, G19. The movement along the stake following the year arrow proceeds according to instruction G202; roll along the stake against the one-year arrow - G203. The stake can be programmed either by varying the radius or by varying the coordinates to the center of the stake.

N... G17 G203 X... Y... Z... I... J... F... S... M...

Let's follow a straight logical path, without getting bogged down in a lot of current international and scientific scientific terms. The coordinate system can be represented as a system that is oriented directly on the surface of the building and the space of the third. To describe the mathematical system, it is represented by two mutually perpendicular lines, called the abscis (X) and ordinate (Y) axes. The smells are oriented horizontally and vertically in the same way. The crossline of these lines is a core of coordinates with zero values in absolute value. And the positioned point on the plane is determined using two coordinates X and Y. In geodesy, the orientation of the axes on the plane is subdivided into mathematics. The planar rectangular system is designated in the X direction for the vertical position (directly towards the bottom) and in the Y direction for the horizontal position (directly towards the outflow).

Classification of coordinate systems

Before the polar systems we can include geographical, astronomical and geodetic, geocentric and topocentric systems.

Geographic coordinate system

The closed surface of the external contour of the Earth is represented by a spheroidal geometric shape. Basically, the direct orientation of the body can be taken to lie on the surface of the body. On the simply presented modified model of our planet in the form of a globe (the figure of the earth), you can visually see the lines in line with the appearance of the Greenwich meridian and the equatorial line.

In this case, the entire system of geographical coordinates is reflected in the world's vast system of geographic coordinates. She introduced the concept of length and breadth. As the degree units of the world loom, the stench becomes a great value. We know a lot about their meaning. It is important to remember that the geographical distance of a particular point is the path between two planes that pass through the zero (Greenwich) meridian and the meridian at the point of expansion, which is indicated. Under the geographical latitude of the point of acceptance of the cut, which is established between the vertical line (or normal) to it and the plane of the equator.

Concepts of astronomical and geodetic coordinate systems and their dimensions

The geographical system intelligently combines the astronomical and geodetic systems. In order to understand the importance of paying attention to the values of geodetic and astronomical coordinates (longitude, latitude, altitude). In the astronomical system, latitude is seen as between the equatorial plane and the vertical line at the point of significance. And the very shape of the Earth in it is seen as a mental geoid, mathematically approximately equal to a sphere. In a geodetic system, latitude is adjusted to the normal to the surface of the earth's ellipsoid at a specific point with the plane of the equator. The third coordinates in these systems give a residual manifestation of the differences. Astronomical (orthometric) altitude is the displacement of the straight line between the actual point and the point on the surface of the level geoid. The geodetic height is determined by the distance between the normal and the surface of the ellipsoid to the point of calculation.

System of flat rectilinear Gauss-Kruger coordinate systems

The skin coordinate system has its own theoretical, scientific and practical economic implications both on a global and regional scale. In certain specific situations, there may be a conflict between reference, spatial and mental coordinate systems, and through mathematical developments and calculations, they can all be interconnected.

p align="justify"> Geodesic rectangular plane coordinate system is a projection of the adjacent six-degree zones of the ellipse. Having inscribed this figure in the middle of a horizontally extended cylinder, the skin area is adjacently projected onto the inner surface of the cylindrical. The zones of such a spheroid are separated by meridians with a width of six degrees. When opened on the surface, a projection emerges, which is named after the German studies that developed Gauss-Kruger. With this method of design, the elements, in some ways, preserve their values. That’s why they sometimes call it sweet. The entire abscise of the zone passes through the center, through the mental axis meridian (all X), and the entire ordinate along the line of the equator (all Y). Dovzhin lines from both sides of the axial meridian are transmitted without interruption, and from both sides of the equatorial line they are transmitted to the edges of the zone.

Polar coordinate system

The more detailed description of the rectilinear coordinate system suggests the presence and inconsistency of the flat polar coordinate system in most geodetic tasks. For the exiting direction, the entire polar (polar) direction, signs and names, will stagnate. To determine the location of the point on the plane, move the polar (directional) path and the radius vector (horizontal) to the point. We guess that the director's kut is respected by the kut that is revived from the exit (outside) direction to the prepared one. The radius vector appears at the designated horizontal alignment. To the spatial polar system, geodetic alignment of the vertical edge and low elevation is added to determine the 3D position of points. This method is practically used today in trigonometric leveling, topographical calculation for the development of geodetic lines.

Geocentric and topocentric coordinate systems

Following the same polar method, the satellite and geocentric geocentric and topocentric coordinate systems are often used, with the difference that the main axes of the trivial space (X, Y, Z) move in different directions. In a geocentric system, the coordinate root is the center of mass of the Earth. All X runs straight from the Greenwich meridian to the equator. All Y is rotated in a rectangular position to the exit in direction X. All Z is initially directed in a polar direction along the minor axis of the elliptical. The coordinates in it are:

in the equatorial plane the convergence of the satellite is geocentric
at the meridian plane there is a geocentric view of the satellite
The geocentric radius vector is from the center of gravity of the Earth to the satellite.

When monitoring the flow of satellites from a standing point on the earth's surface, a topocentric system is created, the coordinate axes of which are extended parallel to the axes of the geocentric system, and the point of guarding is taken into account. Coordinates for this system:

topocentrically more directly than the companion's convergence
topocentric view of the satellite
topocentric radius vector of the satellite
geocentric radius vector at the point of caution.

Current satellite global systems such as WGS-84, PZ-90 include not only coordinates, but also other parameters and characteristics that are important for geodetic systems, security and navigation. Before them lie geodetic and other constants:

Weekend geodetic dates
data from the terrestrial ellipsoid
geoid model
gravitational field model
values of the magnitude of gravitational stationary
The fluidity values are light and different.

Also, using coordinates, AutoCAD can be added to the line at any time and directly. It seems simpler, if there is a prefabricated armchair, for example, such as is shown in Fig. 2.2 We can, having completed calculations, reveal the absolute coordinates of all vertices, and then, using the additional command Vidryzok, create a chair by entering these coordinates from the keyboard. Of course, it is impossible to call this method of folding a chair manually, due to which AutoCAD supports two systems of not absolute, but reference coordinates.

This system is called significant because when a drawing object is created (for example, the lines themselves), as a point from the distance, it is not the origin of coordinates (0,0), but the forward point. Since, for example, the first point of the line has coordinates (100,150), and the line with 200 units of units must be moved to the right from that point horizontally, the coordinates of the other point of the line are equal to (200, 0) – 200 units for the positive direction of the X axis and 0 units for beside the Y axis. The absolute coordinates of this point are aligned (300,150).

This principle is valid for a system of reference Cartesian coordinates, in which the position of a point is described by X and Y coordinates. In a system of reference polar coordinates, its position is described by the distance from the point in front and behind, which is aligned with the horizontal straight line. Most users tend to use the Cartesian coordinate system, but this does not mean that the polar polar coordinate system can be ignored. When working in AutoCAD, you can quickly become confused with the situation when creating an object without a different polar coordinate system will be significantly difficult. We will look at the examples of such situations in section 4.

Whenever you enter reference coordinates, you must precede them with the symbol @ . So, at the pointing position with the armchair line at the reference coordinates, to create another point, the track would have to enter @200.0.

Revealing the symbol @ Tell AutoCAD about those numbers that follow it - these are the values of the coordinates that may be related to the forward points.

Reference Cartesian coordinates

As far back as in school, the Cartesian coordinate system was introduced in the 17th century by the French mathematician Rene Descartes. This system describes the position of a point using horizontal (X) and vertical (Y) coordinates to align with the point (0,0). The absolute Cartesian coordinates are in no way different from the absolute ones, moreover, we are looking not at the origin of the coordinates, but at the forward point. It’s simpler than it seems to show the coordinates, how far from the chosen point of the trace you can draw a line or destroy the object (Fig. 2.6). If the displacement is straight to the left, the X coordinate will be negative. So, if the displacement is straight down, then the Y coordinate will be negative. This system must be completely corrected, since it is visible horizontally and vertically from one point to another. Enter your track coordinates in this format: @ X, Y.

Small 2.6 Cartesian coordinate system

Prominent polar coordinates

In the system of reference polar coordinates, to specify the position of the approach point, the distance between these points (polar radius) and the distance that specifies the direction (polar cut) is determined before the front point. In this case, the polar radius is always taken as a positive quantity. As for the polar edge, then AutoCAD, as the zero axis, is oriented directly to the right (or, as it were, “for three years”), and the polar edge is drawn against the year arrow (Fig. 2.7). In this way, straight uphill (“for twelve years”) is 90°, straight to the left (“for nine years”) is 180°, down (“for six years”) is 270°, and turning around is 270°. 360°

Small 2.7 Reference polar coordinate system

When entering a polar map, the next trace is indicated by the “less” symbol (

Coordinates that indicate the rotation of points, the coordinate system of the screen, are called absolute coordinates. For example, PSET(100,120) means that the screen will have a point 100 pixels to the right and 120 pixels below the top left corner, then. the coordinates on the screen

The coordinates of the point that was painted with the rest are stored in the computer’s memory. This point is called the point of remaining strength (TPS). For example, if, when drawing a line, you indicate only the coordinates of one point, then the screen will display a cut from the TPS to the designated point, after which the TPS itself will appear. Immediately after switching to graphics mode, the remaining point is the point in the center of the screen.

Around the absolute ones, QBASIC uses other coordinates. These coordinates indicate the amount of displacement of the TPS. To paint a new point, vikoryst and reference coordinates, it is necessary to use the keyword STEP(X,Y), where X and Y are the displacement of the coordinates of the TPS.

For example, PSET STEP (-5,10) - at which point a point will appear, the position of which will be left-handed by 5 and 10 points lower than the point of the remaining signal. So, if the point of the remaining position is small in coordinates, for example (100,100), then you see a point with coordinates (95,110).

Painting of lineas and straight cutters.

LINE(X1,Y1)-(X2,Y2),C- Draws a cut that connects points (X1, Y1) and (X2, Y2), color C.

For example, LINE(5,5)-(10,20),4

Result: 5 10

If you do not specify the first coordinate, a trip will be made from the TPS to the point with coordinates (X2, Y2).

LINE(X1,Y1)-(X2,Y2), C, V- Draws the outline of the orthocutaneous with the ends of the diagonal at points (X1,Y1) and (X2,Y2), C - color, B - marker of the orthocutaneous.

For example, LINE(5,5)-(20,20), 5, V

Result: 5 20

If you replace the marker B with BF, then you will be daubed with a rectangular block (block):

LINE(X1,Y1)-(X2,Y2),C, BF

For example, LINE(5,5)-(20,20),5, BF

Result: 5 20

Painting of kels, ellipses and arcs.

CIRCLE(X,Y), R, C- Paints around the center at the point (X, Y), radius R, color C.

For example, CIRCLE(50,50), 10, 7

Result:

CIRCLE(X,Y), R, C, f1, f2- stake arc, f1 and f2 The values of the edges of the arc in radians range from 0 to 6.2831, which indicate the beginning and end of the arc.

CIRCLE(X,Y), R, C, e- ellipse, centered at point (X, Y), radius R, e - the relationship of the vertical axis to the horizontal.

For example, CIRCLE(50,50), 20, 15, 7, 1/2

Result: 30 50 70

If necessary, after parameter C you can specify the values of the cutoffs of the arc ellipse f1 and f2.

PAINT(X,Y), C, K- paint the figure with color Z, daubed with color K (X, Y) - a point that lies in the middle of the figure. Since the color of the outline is consistent with the color of the bar, then indicate only one color: PAINT(X,Y), C

For example, you need to fill the color CIRCLE(150,50), 40, 5 with the color 4. For this requirement, the operator PAINT(150,50), 4, 5 is used, because the center of the stake lies exactly in the middle of the figure that is being prepared, we vikorized it as the internal point.

Version of tasks.

Zavdannya 1.

Draw several points that lie on the same horizontal line at a distance of 20 pixels one at a time. The remaining speck is located at coordinate (15, 20).

Solution: NOTES.

SCREEN 9: COLOR 5.15: REM graphic. mode, background 5, color 15

CLS:REM clearing the screen

PSET(15,20) :REM draws the point at coordinates (15,20)

PSET STEP(20,0) :REM decreases the offset point
PSET STEP(20,0) :REM to remain at 20

PSET STEP(20,0): REM pixels along the OX axis.

Result: 15 35 55 75

20. . . .

Zavdannya 2.

Draw three stakes, the centers of which lie on the same horizontal line at a distance of 30 pixels, one side to the other. The radius of the stake reaches 20, the center of the first stake approaches the center of the screen.

Decision.

SCREEN 9 120 150 180

CIRCLE STEP(0, 0), 20, 15 100

CIRCLE STEP(30, 0), 20, 15

Zavdannya 2.

Stay with the peaks (10,15), (30,25), (30,5) and (20,0).

LINE (10,15)-(30,25), 5

LINE - (30, 5),5

LINE - (25.0), 5

LINE - (10,15), 5

RESULT: 5 10 20 25 30

Write a program to paint a nice picture.

Corisna porada: First start writing the program, paint the picture on a piece of paper in the box and set the required coordinates. You will immediately see what numbers will be used as operands in your program.