CN110826218B - Parameter-based coordinate system implementation method in dynamic geometric software - Google Patents
Parameter-based coordinate system implementation method in dynamic geometric software Download PDFInfo
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Abstract
The invention discloses a parameter-based coordinate system implementation method in dynamic geometric software, which comprises the following steps: creating a user-defined coordinate system which comprises an original point, an X axis, a Y axis, an end point control point, a unit length control point and a data conversion module; the unit length control point is used for changing the unit length of the shaft; the endpoint control point is used for changing the range of the coordinate system on the dynamic geometric canvas page; calculating the positions of the upper left corner and the lower right corner of the grid object according to the attributes of the X axis and the Y axis; the data conversion module is used for matrix transformation of world coordinate system coordinates and target coordinate system coordinates; when the user carries out coordinate conversion, the endpoint control variable or the unit length control variable is calculated, and the offset of the axis, the grid and the data conversion module are modified. The invention supports a multi-coordinate system under the same working environment, can dynamically adjust the range and unit length of the coordinate system and create an unequal ratio coordinate system; a coordinate system with offset origin of coordinates can be implemented.
Description
Technical Field
The invention relates to the technical field of dynamic geometry application software, in particular to a parameter-based coordinate system implementation method in dynamic geometry software.
Background
The application software based on dynamic geometry is mainly used as teaching auxiliary software for mathematics, physics and other disciplines. The coordinate system is a common aid for science. The types of coordinate systems commonly used include cartesian rectangular coordinate systems, planar polar coordinate systems, cylindrical coordinate systems, and spherical coordinate systems. Rectangular and polar coordinates are often used in the plane. It is often necessary to describe the position and orientation of particles by means of a coordinate system, view the pattern in different coordinate systems, compare patterns in multiple coordinate systems, adjust the range of coordinate systems, etc. The existing dynamic geometry software has the following problems:
a. the coordinate system view occupies the whole canvas page and cannot support a multi-coordinate system under the same working environment;
b. the range of the coordinate system and the 1 unit length of the coordinate axis cannot be dynamically adjusted;
c. the origin O (0, 0) cannot be offset to a non-zero position;
therefore, the dynamic geometry software in the prior art does not satisfy teaching applications of different scenes.
Disclosure of Invention
The invention aims to provide a parameter-based coordinate system implementation method in dynamic geometric software, which is used for solving the problems that the dynamic geometric software in the prior art does not support a multi-coordinate system in the same working environment, cannot dynamically adjust the range of the coordinate system and the 1 unit length of a coordinate axis and cannot perform offset operation on an origin O (0, 0) to a non-zero position.
The invention solves the problems through the following technical scheme:
a method for realizing a parameter-based coordinate system in dynamic geometry software comprises the following steps:
creating a user-defined coordinate system, wherein the user-defined coordinate system comprises an original point, an X axis, a Y axis, an end point control point, a unit length control point and a data conversion module;
the unit length control point comprises a unit length control variable and a unit control point, and is used for modifying the unit length of the X axis and/or the Y axis according to the position change of the unit control point before and after dragging;
the endpoint control point comprises an endpoint control variable and an endpoint and is used for changing and modifying the range of the coordinate system in the dynamic geometric canvas page according to the positions of the endpoint before and after being dragged;
the system also comprises a grid object AxisGrid created by an X axis and a Y axis, and the positions of the upper left corner and the lower right corner of the grid object are calculated according to the attributes of the X axis and the Y axis;
the data conversion module is used for converting the world coordinate into the target coordinate system coordinate or converting the target coordinate system coordinate into the world coordinate in dynamic geometric transformation;
when a user drags the endpoint control point or the unit length control point to carry out coordinate conversion, calculating an endpoint control variable or a unit length control variable according to position coordinate conversion, and modifying the offset of the axis, the grid and the data conversion module according to a calculation result; or modify axes, grids, and reset data transformation modules directly according to the offset of the modified axes.
Further, the method for creating the user-defined coordinate system comprises the following steps:
A. selecting a point as an origin and recording the point as O (O _ x, O _ y);
B. designating the X-axis semi-axis length as Lx, the Y-axis semi-axis length as Ly, wherein Lx is more than 0, ly is more than 0;
C. respectively creating two side end point coordinates of an X axis and a Y axis:
creating an end point control variable ax of an X axis, and then multiplying the length of Lx by the value of the end point control variable and adding the X coordinate of an original point O to obtain an X coordinate (Lx _ ax + O _ X) of a right end point XR of the X axis, wherein the y coordinate of the right end point XR of the X axis is O _ y, namely the right end point XR (XR _ X, XR _ y) = XR (Lx _ ax + O _ X, O _ y) of the X axis;
similarly, a left end XL (XL _ X, XL _ y) = XL (0 _x-Lx _, o _ y) of the X axis is created;
creating an endpoint control variable ay of a Y axis, and then multiplying the length of the Ly by the value of the endpoint control variable and adding the Y coordinate of the original point O to obtain the Y coordinate (Ly _ ay + O _ Y) of the upper endpoint YT of the Y axis, wherein the x coordinate of the upper endpoint YT of the Y axis is O _ x, namely the upper endpoint YT (YT _ x, YT _ Y) = YT (0 \ x, ly ay \ + O_y) of the Y axis;
similarly, a lower end point YB (YB _ x, YB _ Y) = YB (0 _x, o _y-Ly ay);
D. respectively creating a unit length control variable u4 of an X axis and a unit length control variable u5 of a Y axis, and calculating the position of a control point of the X axis from the position of an original point O to be called XP (u 4+ O _ X, O _ Y); the unit control point of the Y axis is denoted as YP (o _ x, u5+ o _ Y);
E. create X-axis and Y-axis:
creating an X axis by using the point XL, the origin O, the point XP and the point XR, and recording the X axis as XZ;
creating a Y axis from the point YL, the origin O, the point YP and the point YR, and recording the Y axis as YZ;
attributes are set for an X axis and a Y axis respectively, and the attributes comprise a distance, a unit, whether a number is displayed, whether a scale is displayed, an offset, a position of a distance control scale, whether unit control takes pi as a unit and whether offset control origin point movement is performed;
F. creating a grid object by an X axis and a Y axis and recording the grid object as AxisGrid, and calculating the positions of the upper left corner and the lower right corner of the grid according to the attributes of the X axis and the Y axis by the AxisGrid and recording the positions as leftTop and rightBottom; wherein:
the origin coordinates of the AxisGrid are (o _ X-X axis offset value X axis spacing, o _ Y-Y axis offset value Y axis spacing);
the coordinate of leftTop is (xl _ x, yt _ y), i.e., (o _ x-Lx _ ax, ly _ ay + o _ y);
the coordinates of rightBottom are (xr _ x, yb _ y), i.e., (Lx _ ax + o _ x, o _ y-Ly _ ay);
setting attributes for the grids, wherein the attributes comprise the type of the grids, whether the attributes of the grids are displayed or not and whether the coordinate system is a current use coordinate system or not;
when the user drags the control point to adjust the unit length of the axis and/or the range of the coordinate system is adjusted by the dragging end point control point, the value of the unit length control variable and/or the end point control variable is calculated according to the positions before and after dragging, and the attributes of the axis, the grid and the data conversion module are modified according to the value.
When modifying the offset of the axes, it is necessary to modify the attributes of the axes and the mesh and reset the data conversion module.
Furthermore, the data conversion module attributes comprise an x coordinate offset, a y coordinate offset, an x coordinate scaling ratio and a y coordinate scaling ratio; the attributes are respectively controlled by an X coordinate, a Y coordinate, an X-axis unit and a Y-axis unit of an origin of a target coordinate system;
the data conversion module provides interfaces with:
the transGTS is used for converting the world coordinate into a target coordinate system coordinate;
the transSTS is used for converting the coordinates of the target coordinate system into world coordinates;
reset for resetting the data conversion module.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention supports a multi-coordinate system under the same working environment, can dynamically adjust the range and unit length of the coordinate system and create an unequal ratio coordinate system; a coordinate system with an offset of the origin of coordinates can be implemented.
Drawings
FIG. 1 is a flowchart illustrating a coordinate system implementation of a drag endpoint control point according to the present invention;
FIG. 2 is a flowchart of a coordinate system implementation of a dragging unit length control point;
FIG. 3 is a diagram of the effect achieved by the coordinate system of the control point of unit length dragging the X axis;
FIG. 4 is an effect diagram of setting an anisometric coordinate system;
FIG. 5 is a flow chart of an implementation of axis coordinate shifting;
fig. 6 is a graph showing the effect of axis coordinate shift.
Detailed Description
The present invention will be described in further detail with reference to examples, but the embodiments of the present invention are not limited thereto.
Example 1:
referring to fig. 1, a parameter-based coordinate system implementation method in dynamic geometry software creates a user-defined coordinate system, and the user-defined coordinate system is composed of an origin, four range control points, two unit control points, two axes and a data conversion module. The origin determines the position of a coordinate system. The four range control points control the range of the X-axis and the Y-axis. Two unit control points control the unit length of the X-axis and the Y-axis. The two axes are the X axis and the Y axis of the coordinate system respectively, and the axes have the distance, the unit, whether to display the number, whether to display the scale and the offset attribute. The data conversion module converts world coordinates of the element to coordinates of a target coordinate system.
The user-defined coordinate system creation implementation flow is as follows:
selecting a point as an origin to be marked as O (O _ x, O _ y);
designating a specific datum as a default value of the length of the axis half-axis (the value must be a number greater than 0) and recording the default value as L;
a variable end point control variable is created, the X coordinate (L-end point control variable +0 _x) of the right point of the X axis is obtained by multiplying the length of L by the value of the end point control variable and adding the X coordinate axis of the origin O, the y coordinate of the right point of the X axis is O _ y, and the point is marked as XR (XR _ X, XR _ y).
Similarly, 3 end point control variables are created and respectively calculated to obtain two end points of a left side point of the X axis and the two end points of the Y axis and are sequentially marked as XL (XL _ X, XL _ Y), YT (YT _ X, YT _ Y) and YB (YB _ X, YB _ Y);
creating a variable unit length control variable, calculating the position of a control point of an X axis from the position of an original point and recording the position as XP, wherein the calculation formula of an X coordinate is a unit length control variable + o _ X; the unit control point of the Y axis is recorded as YP, and the calculation formula of the Y coordinate is a unit length control variable + o _ Y;
creating an X axis as XZ by using the points XL, O, XP and XR, creating a Y axis as YZ by using the points YL, O, YP and YR, setting the distance and unit for the axes, displaying numbers or not, displaying scales or offset value attributes, controlling the position of the scales by the distance, controlling whether a triangular coordinate system takes pi as a unit or not by the unit, and controlling the movement of an origin by the offset value;
creating a grid object by an X axis and a Y axis and recording the grid object as AxisGrid, wherein the AxisGrid calculates the positions of the upper left corner and the lower right corner of the grid according to the attributes of the X axis and the Y axis and records the positions as leftTop and rightBottom; setting a grid type (rectangular coordinate system and polar coordinate system), whether to display grid attributes and whether the coordinate system is a currently used coordinate system for the grid;
the data conversion module converts world coordinates into matrix changes of target system coordinates, and the module attributes comprise x coordinate offset, y coordinate offset, x coordinate scaling ratio and y coordinate scaling ratio. The attributes are controlled by X-coordinate, Y-coordinate, X-axis unit, and Y-axis unit of the origin of the target coordinate system, respectively. The module provides interfaces for converting world coordinates into target coordinate system coordinates as transfTS, converting the target coordinate system coordinates into world coordinate system coordinates as transfSTG, and resetting the data conversion module as reset.
The following operations may be performed on the user-defined coordinate system:
1) Dragging the endpoint control point to adjust the coordinate system range, as shown in fig. 1;
dragging the endpoint;
the end-point control variable is calculated,
endpoint control variable = (coordinate value corresponding to endpoint-coordinate value corresponding to origin)/L; wherein L is the half-axis length of the shaft with the end point;
modifying the corresponding coordinate value and the grid according to the calculated endpoint control variable;
a modified data conversion module;
the element position is modified.
For example: dragging the end point control point on the right side of the X axis to adjust the range of the coordinate system, calculating an end point control variable ax,
an end point control variable ax = (the right end point corresponds to an X-axis coordinate value-the origin corresponds to an X-axis coordinate value)/Lx, wherein Lx is the semi-axis length of the X axis;
modifying the corresponding coordinate value and the grid according to the calculated endpoint control variable ax;
if the coordinate system range is adjusted by dragging the endpoint control point on the upper side of the Y axis, the endpoint control variable ay is calculated,
the endpoint control variable ay = (upper endpoint corresponds to Y-axis coordinate value-origin corresponds to Y-axis coordinate value)/Ly, where Ly is the semi-axis length of the Y-axis;
and modifying the corresponding coordinate values, the grids, the data conversion modules and the element positions by the calculated endpoint control variable ay.
2) The drag control point adjusts the unit length of the axis, as depicted in FIG. 2;
a unit length control point on the dragging shaft;
calculating the control variable value of the unit length:
the unit length control variable value = the coordinate value corresponding to the unit point-the coordinate value corresponding to the origin;
modifying the axes and the grids;
and modifying the data conversion module.
If the control point drags the X axis, the unit length control variable u4= the unit point corresponding to the X axis coordinate value-the X axis coordinate value corresponding to the origin; if the control point drags the Y axis, the unit length control variable u5= the unit point corresponding to the Y axis coordinate value-the origin corresponding to the Y axis coordinate value; as shown in fig. 3, a front-to-back comparison graph of the unit length of the axis is adjusted for the control point dragging the X-axis;
3) Setting an anisometric coordinate system
When the unit length control variable u4 of the X axis is not equal to the unit length control variable u5 of the Y axis, the current coordinate system is an anisometric coordinate system, as shown in FIG. 4;
4) Effecting an axis coordinate offset, as shown in FIG. 5;
the offset of the modification axis is 2;
modifying the axes and the grids;
and resetting the data conversion module.
As shown in fig. 6, the X axis is offset to the left by 2 units.
Although the present invention has been described herein with reference to the illustrated embodiments thereof, which are intended to be preferred embodiments of the present invention, it is to be understood that the invention is not limited thereto, and that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the spirit and scope of the principles of this disclosure.
Claims (2)
1. A method for realizing a parameter-based coordinate system in dynamic geometry software is characterized by comprising the following steps:
creating a user-defined coordinate system, wherein the user-defined coordinate system comprises an original point, an X axis, a Y axis, an end point control point, a unit length control point and a data conversion module;
the unit length control point comprises a unit length control variable and a unit control point and is used for modifying the unit length of the X axis and/or the Y axis according to the position conversion before and after the unit control point is dragged;
the endpoint control point comprises an endpoint control variable and an endpoint and is used for changing and modifying the range of the coordinate system in the dynamic geometric canvas page according to the positions of the endpoint before and after being dragged;
the system also comprises a grid object AxisGrid created by an X axis and a Y axis, and the positions of the upper left corner and the lower right corner of the grid object are calculated according to the attributes of the X axis and the Y axis;
the data conversion module is used for matrix transformation of world coordinate system coordinates and target coordinate system coordinates;
when a user drags the endpoint control point or the unit length control point to carry out coordinate conversion, calculating an endpoint control variable or a unit length control variable according to position coordinate conversion, and modifying the offset of the axis, the grid and the data conversion module according to a calculation result;
the method for creating the user-defined coordinate system comprises the following steps:
A. selecting a point as an origin and recording the point as O (O _ x, O _ y);
B. designating the X-axis semi-axis length as Lx, the Y-axis semi-axis length as Ly, wherein Lx is more than 0, ly is more than 0;
C. respectively creating two side end point coordinates of an X axis and a Y axis:
creating an end point control variable ax of an X axis, and then multiplying the length of Lx by the value of the end point control variable and adding the X coordinate of an original point O to obtain an X coordinate (Lx _ ax + O _ X) of a right end point XR of the X axis, wherein the y coordinate of the right end point XR of the X axis is O _ y, namely the right end point XR (XR _ X, XR _ y) = XR (Lx _ ax + O _ X, O _ y) of the X axis;
similarly, a left end XL (XL _ X, XL _ y) = XL (0 _x-Lx _, o _ y) of the X axis is created;
creating an endpoint control variable ay of a Y axis, and then multiplying the length of the Ly by the value of the endpoint control variable and adding the Y coordinate of the original point O to obtain the Y coordinate (Ly _ ay + O _ Y) of the upper endpoint YT of the Y axis, wherein the x coordinate of the upper endpoint YT of the Y axis is O _ x, namely the upper endpoint YT (YT _ x, YT _ Y) = YT (0 \ x, ly ay \ + O_y) of the Y axis;
similarly, a lower end point YB (YB _ x, YB _ Y) = YB (0 _x, o _y-Ly ay);
D. respectively creating a unit length control variable u4 of an X axis and a unit length control variable u5 of a Y axis, and calculating the position of a control point of the X axis from the position of an origin O and recording the position as XP (u 4+ O _ X, O _ Y); the unit control point on the Y axis is denoted as YP (o _ x, u5+ o _ Y);
E. create X-axis and Y-axis:
creating an X axis by using the point XL, the origin O, the point XP and the point XR, and recording the X axis as XZ;
creating a Y axis from the point YL, the origin O, the point YP and the point YR, and recording the Y axis as YZ;
attributes are set for an X axis and a Y axis respectively, and the attributes comprise a distance, a unit, whether a number is displayed, whether a scale is displayed, an offset, a position of a distance control scale, whether unit control takes pi as a unit and whether offset control origin point movement is performed;
F. creating a grid object by an X axis and a Y axis and recording the grid object as AxisGrid, and calculating the positions of the upper left corner and the lower right corner of the grid according to the attributes of the X axis and the Y axis by the AxisGrid and recording the positions as leftTop and rightBottom; wherein:
the origin coordinates of the AxisGrid are (o _ X-X axis offset value X axis spacing, o _ Y-Y axis offset value Y axis spacing);
the coordinate of leftTop is (xl _ x, yt _ y), i.e., (o _ x-Lx _ ax, ly _ ay + o _ y);
the coordinates of rightBottom are (xr _ x, yb _ y), i.e., (Lx _ ax + o _ x, o _ y-Ly _ ay);
and setting attributes for the grid, wherein the attributes comprise the type of the grid, whether the grid attribute is displayed and whether the coordinate system is a current using coordinate system.
2. The method of claim 1, wherein the data transformation module has x-coordinate offset, y-coordinate offset, x-coordinate scaling ratio, and y-coordinate scaling ratio; the attributes are respectively controlled by an X coordinate, a Y coordinate, an X-axis unit and a Y-axis unit of an origin of a target coordinate system;
the data conversion module provides interfaces with:
the transGTS is used for converting the world coordinate into a target coordinate system coordinate;
the transSTS is used for converting the coordinates of the target coordinate system into world coordinates;
reset for resetting the data conversion module.
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