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Description  |
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BACKGROUND OF THE INVENTION
(1) Field of the Invention
The present invention relates to a projection view creation method, and
more specifically, to a projection view creation method of creating a view
by projecting a curved line to a curved surface on a two-dimensional CAD
(computer aided design) system.
(2) Description of the Related Art
A CAD system is indispensable to a design job because a design
specification becomes complex, a design and drawing job must be
effectively carried out, a design period must be shortened and jobs
accompanying the design must be simplified. The two-dimensional CAD system
can optionally create drawings such as a design drawing and the like on a
graphic display screen using basic figure elements such as a straight
line, circle, arc and the like as well as edit created drawings. Further,
when a drawing is completed on the screen, the two-dimensional CAD system
can output the drawing by means of a plotter or the like and contain the
created drawing in a storage medium so that it can be used later.
When the two-dimensional CAD system creates a perspective view from a plan
view, front view and side view, the CAD system can display a
three-dimensional configuration on a two-dimensional screen by projecting
a figure observed from one direction to a figure observed from another
direction. When a process for creating a view by projecting a curved line
to a curved surface is carried out by the CAD system, the view is
conventionally determined by an equation for calculating a shade made by
the projection using equations of the actual curved surface curved line.
As a result, when an element of a new configuration is added as an element
desired to be projected, a unit for processing the equation of the new
configuration is added so that calculation is carried out by an equation
covering the additional configuration.
Nevertheless, in the conventional method of creating a view by projecting a
curved line to a curved surface, since equations for expressing a curved
surface and curved line are very complex, there is a problem that a
program for executing a projection processing also becomes very complex.
Further, since a different equation must be used to express a curved line
to be projected or a curved surface to which projection is effected, there
is also a problem that an exclusive program must be created in accordance
with the curved line and the curved surface.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a projection view creation
method which need not prepare a calculation formula for each figure to be
subjected to a projection processing and can prevent a program for
executing the projection processing from being made complex.
To achieve the above object, there is provided a projection view creation
method of creating a projection view by projecting a curved line to a
curved surface. The projection view creation method comprises the steps of
dividing and converting a curved line to be projected and the curved line
representing the cross section of a curved surface to which projection is
effected into a first broken line and a second broken line each composed
of a group of straight lines, creating two vectors directed to the first
broken line from the both ends of one of the straight lines of the second
broken line, and projecting one of the straight lines constituting the
first broken line to a plane having the straight line constituting the
second broken line as its side within the range designated by the two
vectors.
The above and other objects, features and advantages of the present
invention will become apparent from the following description when taken
in conjunction with the accompanying drawings which illustrate preferred
embodiments of the present invention by way of example.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a flowchart showing the principle of a projection view creation
method according to the present invention;
FIG. 2 is a flowchart showing a processing for projecting an ellipse to a
curved surface represented by a spline curve;
FIG. 3 is a view showing a display on a screen effected by a
two-dimensional CAD system by way of example;
FIG. 4 is a view showing a data structure of an ellipse by way of example;
FIG. 5 is a view showing a data structure of a spline curve by way of
example;
FIG. 6 is a view showing a data structure of a broken line by way of
example;
FIG. 7 is a view showing a state that a curved line is converted into a
group of straight lines by way of example;
FIG. 8 is a view showing a state that a curved surface is converted into a
group of planes by way of example;
FIG. 9 is a flowchart showing a projection process when a straight line is
projected to a plane;
FIG. 10 is a view showing an image when a first vector is created;
FIG. 11 is a view showing an image when second and third vectors are
created;
FIG. 12 is a view showing a positional relationship of projection when a
first broken line is projected to a second broken line;
FIG. 13 is a display on a screen of a created projection view by way of
example;
FIG. 14 is a view explaining a method of projecting a straight line to a
plane; and
FIG. 15 is a block diagram showing a hardware arrangement of a work station
embodying the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
An embodiment of the present invention will be described below with
reference to the drawings.
FIG. 1 is a flowchart showing the principle of a projection view creation
method according to the present invention.
According to the projection view creation method of the present invention,
first, a curved line to be projected and a curved line representing the
cross section of a curved surface to which projection is to be effected
are finely divided and converted into first and second broken lines each
composed of a group of straight lines, respectively at step S1. Next, at
step S2, a first vector is created from an end of one of the straight
lines constituting the first broken line toward a direction in which the
first vector intersects a plane having one of the straight lines of the
second broken line as its side. At step S3, second and third vectors are
created from the two ends of the straight line of the second broken line
constituting one edge of the plane intersecting the first vector. Then, at
step S4, the first broken line within the range designated by the second
and third vectors is projected to the plane having the straight line of
the second broken line as its side.
According to the projection view creation method, the curved line to be
projected and the curved line representing the cross section of the curved
surface to which projection is to be effected are previously divided into
the groups of straight lines and these groups are converted a first broken
line and a second broken line, respectively. With this processing, the
curved line to be projected is converted into an aggregation of the
straight lines, and the curved surface to which projection is to be
effected is converted into an aggregation of planes. Thereafter, a
projection processing is carried out with respect to the straight lines
constituting the broken lines.
The first vector is created from an end of one of the divided straight
lines of the first broken line, i.e., from one of the vertices of the
broken line toward a direction in which the first vector intersects a
plane having a side composed of one of the straight lines of the second
broken line to determine a straight line of the second broken line of the
plane intersecting the first vector. Next, projection is carried out from
the first broken line within the range designated by the second vector and
the third vector to a group of planes.
FIG. 2 is a flowchart showing a processing for projecting an ellipse to a
curved surface represented by a spline curve.
When the ellipse is to be projected to the curved surface represented by
the spline curve by the two-dimensional CAD system, a process enters a
main program for executing a projection processing, and a first program
PROG1 processes the previously indicated ellipse to convert it into a
first broken line. In the same way, the first program PROG1 processes the
previously indicated spline curve to convert it into a second broken line.
Note, the first program PROG 1 is a module for converting a circle, arc,
ellipse, elliptic arc and spline curve into a broken line.
Next, data of the first broken line and the second broken line converted by
the first program PROG1 is processed in a loop. A second program PROG2 as
a module for projecting a straight line to a plane receives data of the
respective sides of the first broken line and the second broken line to
subject the sides to a projection processing so that a straight line when
the first broken line is projected to a plane having a straight line of
the second broken line as its side is determined. This processing is
repeated with respect to all the straight lines constituting the first
broken line.
When all the straight lines of the first broken line are projected, a
projection view is displayed on a screen by a third program PROG3 as a
module for displaying straight lines on the screen.
FIG. 3 is a view showing a display on a screen effected by the
two-dimensional CAD system by way of example. The display example shows a
portion of the views of a product observed from three sides, i.e., a right
side view is displayed on the right side of the screen and a front view is
displayed on the left side thereof.
When a projection view is to be created by projecting an ellipse CL1 at the
center of the right side view to a curved surface whose contour is formed
by a spline curve CL2 of the front view, first, the spline curve CL2 is
indicated by the operation of a designer and thereafter the ellipse CL1 is
indicated. Then, the main program for carrying out the projection
processing receives the information of the ellipse CL1 and the spline
curve CL2 by means of the element numbers of them and supplies the
information to the first program PROG1.
For example, when it is supposed that the element number of the ellipse CL1
is "1001", the first program PROG1 searches a database based on the
element number and fetches the data of the ellipse CL1. In the same way,
when it is supposed that the element number of the spline curve CL2 is
"1002", the first program PROG1 searches the database based on the element
number and fetches the data of the spline curve CL2.
FIG. 4 is a view showing a data structure of an ellipse by way of example.
The data of the ellipse has the same structure as that of the data of an
elliptic arc and is composed of a center x-coordinate of the ellipse,
center y-coordinate thereof, inclination of the ellipse represented by an
angle between a horizontal axis passing through a center coordinate and a
major axis, length of the major axis, length of a minor axis, start angle
representing an end of the elliptic arc and terminate angle representing
the other end of the elliptic arc. In the case of an ellipse, the start
angle is fixed to 0.degree. and the terminate angle is fixed to
360.degree..
FIG. 5 is a view showing a data structure of a spline curve by way of
example. The spline curve is composed of the number of vertices
representing the number of connections of fine line segments constituting
the spline curve, start point of the spline curve, terminate point of the
spline curve, start time and terminate time, x- and y-coordinates of a
vertex 1 . . . , x- and y-vectors of the vertex 1 and interval length 1-2,
. . .
FIG. 6 is a view showing a data structure of a broken line by way of
example. The first program PROG1 converts the ellipse and the spline curve
into broken lines, respectively based on the data thereof fetched from the
database and outputs the ellipse and the spline curve in the common form
of broken line data. The data of the ellipse and the spline curve are
divided into a plurality of straight lines by the processing for
converting them into the broken lines and thus the broken line data are
represented by the coordinates at both ends of the respective divided
straight lines. More specifically, the broken line data are represented by
the x-coordinate of the vertex 1, the y-coordinate of the vertex 1, . . .
At that time, the first program PROG1 also supplies the number of the
vertices to the main program together with the coordinates of the
vertices.
FIG. 7 is a view showing a state wherein a curved line is converted into a
group of straight lines by way of example. The illustrated example uses an
ellipse as the curved line and is exaggeratedly shown to some degree by
reducing accuracy when the ellipse is divided into a group of straight
lines constituting a broken line for the convenience of description. The
ellipse CL1 is converted into six straight lines L1-L6 here by the first
program PROG1.
FIG. 8 is a view showing a state wherein a curved surface is converted into
a group of planes by way of example. Here, the spline curve CL2 stored in
the CAD system as data is divided into a group of straight lines to show a
spline surface including the spline curve CL2 by an image divided into a
group of planes. In the illustrated example, the spline surface is
converted into five planes S1-S5 by the first program PROG1.
Next, on the completion of the conversion of the curved line to be
projected into the group of the straight lines and the conversion of the
curved surface to which projection is effected into the group of the
planes as described above, a projection processing is carried out using
the group of the straight lines and the group of the planes. The sequence
of the projection processing will be described below. When the projection
processing is carried out, the main program successively supplies the
coordinates of the ends of the respective straight lines determined from
the curved line and the coordinates of the ends of the straight line
representing a side of the planes determined from the contour of the
curved surface to the second program PROG2 for processing. The straight
lines created by the projection processing are supplied to the main
program in terms of the values representing the coordinates of the ends of
the straight lines.
FIG. 9 is a flowchart showing a projection processing when a straight line
is projected to a plane. Here, a curved line to be projected, which is,
for example, composed of an ellipse is divided into a plurality of
straight lines, a curved line approximated by these straight lines is
represented by a first broken line 1, the vertices of the first broken
line 1 are successively represented by m=0, 1, . . . , and an arbitrary
one of the straight lines is represented by m. On the other hand, with
respect to the curved surface to which projection is effected, a spline
curve, for example, which represents the cross section of the curved
surface is divided into a plurality of straight lines and a curved line
approximated by these straight lines is represented by a second broken
line 2 and an arbitrary one of the straight lines is represented by n.
First, a first vector V1 is tentatively created from the vertex m=0 of the
first broken line 1 to the curved surface (step S11). Next, it is
determined whether the first vector V1 is directed toward a direction in
which the vector intersects plane the of the second broken line 2 (step
S12) having a straight line n=0"; as its side. When the first vector V1 is
not directed toward the direction in which the vector intersects the plane
having the straight line n the vertex of the first broken line 1 is
shifted to the next vertex of the first broken line 1 and the first vector
V1 is created from the vertex m=1 of the first broken line 1 (step S13).
As described above, the first vector V1 is repeatedly created by changing
the position of the vertex until it intersects the curved surface composed
of the second broken line 2.
FIG. 10 is a view showing an image when the first vector is created. The
illustrated example shows a state that the first vector V1 is created from
the vertex m=0 of the first broken line 1. When the first vector V1 does
not intersect any of the planes composed of the second broken line 2, the
first vector V1 is created from the next vertex.
Returning to FIG. 9, next, when the first vector V1 intersects the plane
having the straight line n of the second broken line 2 as its side, second
and third vectors V2 and V3 are created from both ends of the straight
line n to the first broken line 1 (step S14).
FIG. 11 is a view showing an image when the second and third vectors are
created. In the illustrated example, second and third vectors V2 and V3
are created from the both ends of the straight line, for example, the
straight line n of the second broken line 2 constituting side of the plane
intersecting the first vector V1 from to the first broken line 1.
Returning to FIG. 9 again, the straight line m whose end point is the
vertex from which the first vector V1 is created to the plane having the
straight line n as its side edge (step S15). Next, it is determined
whether the straight line m is final or not (step S16). When the straight
line m is final, the projection processing is finished and the process
quits the loop.
When the projected straight line m is not final, it is determined whether
the other point end points of the straight line m goes outside of the
range designated by the second and third vectors V2 and V3 (step S17).
When the other end point of the straight line m does not go outside of the
range designated by the second and third vectors V2 and V3, the next
straight line m+1 is projected (step S18). When the other end point of the
straight line m goes outside of the range designated by the second and
third vectors V2 and V3, the process is started again from the step that
the plane to which projection is to be effected is shifted to the side
where the straight line is out of the range and the second and third
vectors V2 and V3 are determined again based on the straight line n.+-.1
constituting the side of the plane where the straight line is out of the
range (step S19). If the planar surface whose side is represented by
straight line n is the first or final plane (i.e., all planes have ben
processed--step S20), then any remaining straight line segment m inside
the range of V2 and V3 of the first or final place are also projected
(steps S21-S23).
FIG. 12 is a view showing a positional relationship of projection when the
first broken line is projected to the second broken line. Note, although
the second broken line 2 is observed just from the transverse direction
thereof, the first broken line 1 is observed from a slightly upper
direction so that it can be easily observed.
According to the aforesaid projection processing, first, a straight line L1
is projected to a plane S2. Next, the straight line L1 is projected to a
plane S3. Thereafter, the straight line L1 is projected to a plane S4, a
straight line L2 is projected to a plane S5, a straight line L3 is
projected to the plane S5, a straight line L4 is projected to a plane S4,
the straight line L4 is projected to the plane S3, the straight line L4 is
projected to the plane S2, the straight line L5 is projected to the plane
S1, and a straight line L6 is projected to the plane S1, in the same way.
Since the projection processing is carried out only to the locations where
the curved surface to which the projection is to be effected exist, it
suffices only to repeat the projection processing ten times in the
illustrated example. Incidentally, in a conventional method, the
projection processing must be repeated 6.times.5=30 times when the first
broken line 1 is divided into six sections and the second broken line 2 is
divided into five sections.
FIG. 13 is a view of a display on the screen of a created projection view
by way of example. The data of a broken line composed of a group of
straight lines having been subjected to the projection processing are
supplied from the main program to a third program PROG3 together with the
number of vertices and the projection view is displayed on the screen.
According to this display example, when the spline curve CL2 and the
ellipse CL1 are indicated, the ellipse CL1 is projected to the curved
surface whose contour is formed by the spline curve CL2 and a perspective
view obtained when a product is observed from an obliquely upper direction
is drawn, for example, below the projected ellipse CL1.
Next, a calculation effected by the method of projecting a straight line to
a plane will be described by way of example.
FIG. 14 is a view explaining the method of projecting a straight line to a
plane. FIG. 14 shows an example in which the straight line L10 illustrated
by a thick line of a right side view shown on the right side of the FIG.
14 is projected to the plane S10 illustrated by a thick line of a triangle
of a front view shown on the left side of the FIG. 14. The respective
vertices of the triangle have coordinates, for example, (0, 0) , (0, 7),
and (5, 0) and the respective vertices of the right side view have
coordinates, for example, (0, 0), (0, 7), (4, 7) and (4, 0). Although
there are two coordinates (0, 0) in FIG. 14, this is because the front
view and the right side view are drawn on a different coordinate system.
First, the point (4, 7) which is one of the end points of the straight
line L10 is projected to the plane S10.
First, a direction vector of the plane S10 is determined. The direction
vector is determined from the coordinates of the two points of the front
view by (0-5, 7-0)=(-5, 7).
Next, a normal vector is determined from the direction vector. When it is
assumed here that the normal vector is (a, b), -5a+7b=0 is established
from the aforesaid direction vector. When a=7, b=5 is obtained, from which
one of the normal vectors can be made to be (7, 5). When this is expressed
by a three-dimensional vector, (7, 5, 0) is obtained.
Next, a plane equation of the plane S10 is determined. When the plane
equation is assumed as follows,
ax+by+cz+d=0 (1)
since the normal vector is represented by (7, 5, 0), 7x+5y+d=0 is obtained.
Since the plane S10 passes through the point (0, 7), 35+d=0, that is,
d=-35 is obtained. Thus, the following plane equation of the plane S10 is
obtained.
7x+5y-35=0 (2)
Here, a three-dimensional straight line passing through the point (4, 7) of
the right side view and perpendicular to the right side view is
considered. It is assumed here that the coordinates of the both ends of
the straight line are represented by (4, 7, 20) , (4, 7, 20) in terms of
three dimension when a length in the Z-direction is tentatively determined
"20". When the coordinates are multiplied by a rotation matrix indicating
a right side, the following equation is obtained.
##EQU1##
Thus, the coordinates of the both ends of the straight line are (20, 7, -4
) , (-20, 7, -4 ) when expressed accurately.
Next, a point of intersection of the previously determined
three-dimensional straight line and the plane is determined. The point of
intersection of the plane and the straight line is expressed by the
following equation.
P=P0+(S0/(S0-S1)) (P1-P0) (4)
where, P is a point of intersection, P0 is the start point of a straight
line (=(20, 7, -4)), P1 is the terminate point of the straight line
(=(-20, 7, -4)), SO is a value (=140 +35 -35 =-140) obtained by
substituting the start point P0 of the straight line for the plane
equation (equation 2), and S1 is a value (=-140+35-35=-140) obtained by
substituting the terminate point P1 of the straight line for the plane
equation (equation 2). Thus, the point of intersection P is expressed by
the following equation.
P=(0, 7, -4) (5)
As a result, the point (4, 7) of the right side view is represented by (0,
7, -4) in terms of three-dimension.
Next, the thus determined three-dimensional coordinates are returned to
two-dimensional coordinates. When they are returned to the two-dimensional
coordinates, from which direction a view is to be observed is
predetermined. Since the view is usually drawn so that it is obliquely
observed (isometric view) in many cases, however, when a rotation matrix
indicating the isometric view is multiplied, the following equation is
obtained.
##EQU2##
As a result, a coordinate when one of the points (4, 7) of the straight
line L10 of the right side view is projected is obtained. In the same way,
a coordinate when the other point (4, 0) of the straight line L10 of the
right side view is projected is also obtained. A view when the straight
line L10 of the right side view is projected to the plane S10 of the front
view is obtained by drawing a straight line using these coordinates.
FIG. 15 is a block diagram showing a hardware arrangement of a work station
embodying the present invention by way of example. In FIG. 15, the work
station is composed of a processor 11, a read only memory (ROM) 12, a main
memory (RAM) 13, a graphic control circuit 14, a display device 15, a
mouse 16, a keyboard 17, a hard disk drive (HDD) 19, a magnetic tape drive
(MTD) 20, a plotter 21, a printer 22, and a color hard copy device 23.
These components are interconnected through an interface controller (not
shown) and a bus 24.
The processor 11 integrally controls the workstation as a whole. The read
only memory 12 stores, for example, a program necessary for start up and
the like. The main memory 13 includes a system program, application
programs for a two-dimensional CAD system and the like which are developed
therein as well as creates and stores drawings, projected views, data
being edited and the like.
The graphic control circuit 14 includes a frame memory and the like,
converts various figure element data such as two-dimensional line segment
data, circle data, arc data, elliptical arc data, spline curve data,
projected view data and the like into display signals and supplies the
display signals to the display device 15. The display device 15 displays a
view composed of the figure elements based on the received display
signals.
The mouse 16 is a pointing device for moving a cursor displayed on the
screen of the display device 15, hitting a figure element displayed on the
screen when a button is clicked and indicating the selection of various
menus. In particular, when a projected view is to be created, the mouse 16
is used to indicate elements to be projected and a plane to which
projection is effected. The keyboard 17 is used to input numerical data
such as a value for indicating a length of a straight line by which a
curved line is divided, and the like.
The hard disk drive 19 stores the system program, the application programs
including a program for crating a projected view by the two-dimensional
CAD system, various figure element data necessary to make drawings, a
search range setting table and the like. The magnetic tape drive 20 is an
external memory device capable of inputting data such as design drawings
and the like stored in a magnetic tape 20a and storing data such as
created design drawings and the like to the magnetic tape 20a.
Further, the data of created design drawings can be output through the
plotter 21, the printer 22 or the color hard copy device 23.
As described above, according to the present invention, a curved line to be
projected is divided into a group of straight lines and a curved surface
to which projection is effected is divided into a group of planes so that
they can be represented by common figure elements without depending upon
particular figures, a first vector is created from a broken line composed
of the straight lines and a plane intersecting the first vector is
searched, second and third vectors are created from a plane intersecting
the first vector to the broken line, and the straight lines of the broken
line are projected to the planes within the ranges designed by these
vectors.
As a result, a calculation formula applied to each figure to be subjected
to a projection processing need not be prepared and thus a program can be
made relatively simple. Further, since only straight lines which must be
subjected to the projection processing are projected, the number of
repetition of projecting lines can be greatly reduced so that the speed of
the projection processing can be increased. Further, curved surfaces and
curved lines which cannot be processed up to now can have been processed
by only the addition of a processing for converting them into a plane and
straight line.
The foregoing is considered as illustrative only of the principles of the
present invention. Further, since numerous modifications and changes will
readily occur to those skilled in the art, it is not desired to limit the
invention to the exact construction and applications shown and described
and accordingly, all suitable modifications and equivalents may be
regarded as falling within the scope of the invention in the appended
claims and their equivalents.
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