CN85107564A - The stereoplotter of aphylactic map projection direction - Google Patents

The stereoplotter of aphylactic map projection direction Download PDF

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CN85107564A
CN85107564A CN 85107564 CN85107564A CN85107564A CN 85107564 A CN85107564 A CN 85107564A CN 85107564 CN85107564 CN 85107564 CN 85107564 A CN85107564 A CN 85107564A CN 85107564 A CN85107564 A CN 85107564A
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perspective
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angle
coordinate diagram
angle perspective
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陈无逸
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Abstract

The invention belongs to mapping, Graphing of Engineering and painting skill field, be exclusively used in drawing and the teaching demonstration aspect of perspective view, positive shaft survey, wide-angle perspective figure.
Existing scenography and positive shaft survey method fail to set up definite space coordinates, and general drawing step is loaded down with trivial details, and wherein the angular field of view in the scenography also is subjected to artificial restriction.
The present invention is made up of coordinate diagram and a curve ruler that horizontal coordinate show some width of cloth.Use the present invention, can directly determine vanishing point position, axial rake and the axial stretching rate of body outline when any projecting direction, and can draw wide-angle perspective figure.

Description

The stereoplotter of aphylactic map projection direction
The invention belongs to mapping, Graphing of Engineering and painting skill field, and be specifically designed to drawing and the teaching demonstration aspect of perspective view, positive shaft survey, wide-angle perspective figure.
The number form notion of existing scenography is fuzzyyer, fail to set up definite space coordinates, whenever projecting direction (pitch angle, when the azimuth) changing, all need adopt the mapping or the computational methods of tired lock could determine the vanishing point position of body outline on picture; Existing positive shaft survey method also fails to set up definite space coordinates, when projecting direction changes, also need adopt the calculating or the drawing method of tired lock just can draw axial rake and axial stretching rate; In addition, the angular field of view in the existing scenography also has to be limited.
The stereoplotter that the purpose of this invention is to provide a kind of aphylactic map projection direction.This plotter is made up of some width of cloth coordinate diagram and a curve ruler, have simple structure, low, the convenient carrying of cost, and operation technique is grasped easily, can simplify the stereogram drawing technique, can improve the graphics theory level again, therefore, relevant works technical staff, teacher, student, art worker and drawing fan are generally accepted, thereby can produce in enormous quantities.
A, relevant nominal definition and symbol are enumerated
Viewpoint---observer's eye position, O represents with symbol.
Sight line---from the viewpoint to the visual field in the general designation of the straight line that draws of arbitrfary point.
The sight line of the main line of sight---direction of gaze.
Visual angle---the angle of the arbitrary sight line and the main line of sight is represented (attention is different from traditional perspective definition) with symbol theta.
Picture---the plane vertical with the main line of sight.
Picture in picture---the certain viewing angles scope.
The intersection point of principal point---the main line of sight and picture is used symbol O ' expression.
Draw distance---viewpoint is to the distance of principal point, and R represents with symbol.
The side trunnion axis---cross viewpoint, and be parallel to the horizontal line of picture, OX represents with symbol.
Positive trunnion axis---cross viewpoint, and the horizontal line vertical with the side trunnion axis, OY represents with symbol.
Vertical axes---cross the plumb line of viewpoint, OZ represents with symbol.
Ground level---cross the horizontal plane (attention is different from actual ground) of viewpoint.
Positive facade---by the plane of side trunnion axis and vertical axes decision.
Side elevation---by the plane of positive trunnion axis and vertical axes decision.
View plane---by the plane (face upward, be the inclined plane when overlooking, overlap with ground level when looking squarely) of the main line of sight and the decision of side trunnion axis.
Pitch angle---claim elevation angle again, promptly the angle of cut of the main line of sight and ground level is used symbol 0Expression (wherein the elevation angle is for just, and the angle of depression is for bearing).
The angle of cut of inclination angle (latitude)---arbitrary straight line in space (comprising sight line) and ground level is represented (wherein near low Gao Weizheng far away, nearly farsighted hanging down is negative) with symbol .
Azimuth (longitude)---the trace of the arbitrary straight line in space (comprising sight line) on ground level and the angle of cut of side elevation represented (wherein trace is right far for just, and is left far away right near for bearing) in the vicinity with sign of lambda.
Former line---be parallel to the straight line of picture.
The horizon---claim 0 ° of parallel again, i.e. the intersection of ground level and picture.
The intersection of eye-level display---view plane and picture.
Vanishing point---be parallel to the sight line of the arbitrary straight line in space and the intersection point of picture, be called the vanishing point of this straight line.
Wide-angle perspective figure---object exceeds the perspective view that 30 ° of visual angles (i.e. 60 ° of alleged visual angles of tradition) are done.In order to reduce perspective distortion, can adopt generalized projection (can be regarded as sight line is refracted on the picture by the lens that certain is similar to the eyeball dioptric system), what the present invention adopted is azimuthal projection moderate distance projection (also being a kind of generalized projection), and consequent wide-angle perspective figure is similar to wide-angle photography.
The horizontal system of coordinates---with the viewpoint is the center, length is made ball for radius arbitrarily, the intersection of life side elevation and this sphere is 0 ° of warp, the intersection of ground level and this sphere is 0 ° of parallel (being the horizon), and the upper and lower intersection point of vertical axes and this sphere divides another name zenith, nadir.Aforesaid azimuth and inclination angle are seen in longitude (λ), latitude () definition.
Visual field spherical polar coordinates system---with the viewpoint is the center, long arbitrarily is radius, make hemisphere in field range (only front space), the life main line of sight is a limit with this hemispherical intersection point, view plane and hemispherical intersection are the spherical polar coordinates axle, (counterclockwise for just, clockwise direction is for bearing) represented with symbol in the spherical polar coordinates azimuth, and zenith distance (being the visual angle) is represented (be on the occasion of) with symbol theta.
Polar coordinate system in the plane---the intersection point of the life main line of sight and picture is limit (being principal point), and eye-level display is a pole axis, and polar angle is represented (counterclockwise for just, clockwise direction is to bear) with δ, and pole span is represented (be on the occasion of) with ρ.
Visual field rectangular coordinate system---by side trunnion axis OX, positive trunnion axis OY, the rectangular coordinate system in space that vertical axes OZ forms.
B, relevant coordinate transform formula are enumerated
(, (α, formula θ) is horizontal coordinate λ) to be transformed into visual field spherical polar coordinates wherein 0Be pitch angle.
(α, (δ, ρ), functional relation is the visual field spherical polar coordinates θ) to be transformed into plane polar coordinates
Figure A8510756400061
When perspective projection, (2) formula is
Figure A8510756400062
When normal axonometric projection, (2) formula is
Figure A8510756400063
When wide-angle perspective projection, (2) formula is
Figure A8510756400064
Wherein R is the picture distance.
((, formula λ) is the visual field rectangular co-ordinate z) to be transformed into horizontal coordinate for x, y
Figure A8510756400065
Look squarely (is 0=0 °) time, (, (α, formula θ) is horizontal coordinate λ) to be transformed into visual field spherical polar coordinates
Figure A8510756400066
The making of C, stereoplotter
Stereoplotter is divided into perspective grid figure (press the pitch angle difference and be some width of cloth); Positive axis is surveyed coordinate diagram (press the pitch angle difference and be some width of cloth); Wide-angle perspective coordinate diagram (press the pitch angle difference and be some width of cloth); Straightedge body perspective grid figure (width of cloth); Straightedge body positive axis is surveyed coordinate diagram (width of cloth); Straightedge body wide-angle perspective coordinate diagram (width of cloth); Wide-angle perspective curve ruler (one).
The making of perspective grid figure: press earlier pitch angle ( 0) certain between diaphragm density (for example being separated by 5 °), be equipped with some width of cloth paper or flat board, each pitch angle is a width of cloth, and plane polar coordinates is inscribed on this plane; Using formula (1) and formula (2-1) again, the projection of drawing out horizontal coordinate on this plane marks longitude and latitude.
Positive axis is surveyed the making of coordinate diagram: replace perspective grid figure with formula (2-2) and make interior formula (2-1), other preparation methods are identical with it.
The making of wide-angle perspective coordinate diagram: replace perspective grid figure with formula (2-3) and make interior formula (2-1), other preparation methods are identical with it.
The making of straightedge body perspective grid figure: be equipped with a width of cloth paper or a flat board earlier, plane polar coordinates is inscribed on this plane, life =0 ° and =± 90 °, using formula (1) and formula (2-1) again are with all certain intervals density (for example being separated by 5 °) pitch angle ( 0) time horizon, the zenith, the projection of nadir that produce all be plotted on this plane, mark the longitude on " * degree horizon, the elevation angle (or angle of depression) " and " * degree elevation angle zenith " or " * spend angle of depression nadir " printed words and the horizon.
Straightedge body positive axis is surveyed the making of coordinate diagram: replace straightedge body perspective grid figure with formula (2-2) and make interior formula (2-1), other preparation methods are identical with it.
The making of straightedge body wide-angle perspective coordinate diagram: replace straightedge body perspective grid figure with formula (2-3) and make interior formula (2-1), other preparation methods are identical with it.
The making of wide-angle perspective curve ruler.The wherein making of shape: be about straightedge body wide-angle perspective coordinate diagram diameter in length, width is about on the square transparent panel of a block length of straightedge body wide-angle perspective coordinate diagram radius, the horizon shape copying of certain intervals on the straightedge body wide-angle perspective coordinate diagram (it is better close to heal at interval) is come out, carve the wire casing of sky again by its shape, the wire casing width can put in drawing pen nib and be as the criterion; Wherein scale is made: establish straightedge body wide-angle perspective coordinate diagram and vertically place, it is parallel with this coordinate diagram to establish a plane again, make straight line grid in length and breadth more in the plane, so, visual field rectangular co-ordinate (the x of each intersection point in this grid, y, z) just can determine, using formula (3) again, make it be transformed into horizontal coordinate (, λ), using formula (4) again, make horizontal coordinate be transformed into visual field spherical polar coordinates (α, θ), using formula (2-3) again, make visual field spherical polar coordinates be transformed into plane polar coordinates (δ, ρ), pass through trace-point method again, on straightedge body wide-angle perspective coordinate diagram, make the wide-angle perspective projection (referring to Figure 14) of vertical straight line in the grid, like this, horizon in the straightedge body wide-angle perspective coordinate diagram is divided into plurality of sections (not five equilibrium) by vertical straight line, again according to these section lengths, makes scale (referring to Figure 15) on the wide-angle perspective curve ruler.
D, use and description of drawings
Determining of rule 1 vanishing point position: if inclination angle, the azimuth of a certain straight line in space are known, then its vanishing point position must and be same as on the intersection point of azimuthal warp at the parallel that is same as the inclination angle.
Determining of the axial rake of rule 2 normal axonometric projections and axial stretching rate: if the vanishing point position of a certain straight line in space is definite, then axial rake δ and axial stretching rate μ equal vanishing point is surveyed the polar polar angle δ of coordinate diagram midplane and pole span ρ and coordinate diagram radius R at positive axis ratio (if the coordinate diagram radius is 1, then pole span length is exactly expansion and contraction) respectively.
Other selection of rule 3 projection-type: if object (comprising the object group) in about 5 ° angular field of view the time, should be selected normal axonometric projection; If object in about 30 ° of angulars field of view the time, should be selected perspective projection; If when object surpasses 30 ° angular field of view, should select wide-angle perspective projection.
Selecting for use of rule 4 coordinate diagram: if the straightedge body (comprising cuboid) that object is made up of horizontal line and vertical curve regardless of pitch angle, is all selected a width of cloth straightedge body coordinate diagram for use; If object is polyhedron (promptly having the inclined plane), then select a wherein width of cloth coordinate diagram for use by pitch angle; During application, multiple translucent drawing paper on coordinate diagram earlier.
The use of rule 5 wide-angle perspective curve rulers: if 2 of a, b are certain wide-angle perspectives of 2 on the space line, the wide-angle perspective that describe this straight line needs to express with curve ruler.Earlier the principal point on the curve ruler is aimed at the principal point 0 ' on the wide-angle perspective coordinate diagram, rotating curve plate again, make a, b at 2 all in a certain wire casing of curve ruler, connect a, b 2 points with drawing pen in this wire casing again, the lines of being drawn are exactly the wide-angle perspective of this space line.Scale on the curve ruler is used to express the wide-angle perspective length of former line (straight line that is parallel to picture).
Example one: inclination angle =30 of a known parallax °, azimuth λ=45 °, angle of depression 0=-30 °, selected perspective projection.Requirement is selected coordinate diagram and is determined the vanishing point V of this straight line.
According to rule 4, select " 30 ° of angle of depression perspective grid figure " for use; According to rule 1, find out the intersection point of 30 ° of parallels and 45 ° of warps, the vanishing point V that this point is exactly this straight line.
Example two: azimuth λ=-60 of a known horizontal line (be inclination angle =0 °) °, angle of depression 0=-15 °, selected wide-angle perspective projection.Requirement is selected coordinate diagram and is determined the vanishing point V of this straight line.
According to rule 4, select " straightedge body wide-angle perspective coordinate diagram " for use; According to rule 1, find out-60 ° of longitude this point on " horizon, 15 ° of angles of depression " (i.e. 0 ° of parallel), the vanishing point V that this point is exactly this straight line.
Example three: azimuth λ=60 of a known horizontal line (be inclination angle =0 °) °, angle of depression 0=-45 °, selected normal axonometric projection.Requirement is selected coordinate diagram and is determined the vanishing point V of this straight line, and asks the axial rake δ and the axial stretching rate μ of this straight line.
According to rule 4, select " straightedge body positive axis is surveyed coordinate diagram " for use; According to rule 1, find out the last 60 ° of longitude this point of " horizon, 45 angle of depression " (i.e. 0 ° of parallel), the vanishing point V that this point is exactly this straight line; Connect VO ' (O ' be principal point) again, like this,, on the plane polar coordinates of coordinate diagram, just can draw axial rake δ=22.5 °, axial stretching rate μ=0.94 according to rule 2.
Fig. 1 is the wide-angle perspective figure that selects for use " 60 ° of elevation angle perspective grid figure " to be drawn, and it has shown the vanishing point position of the diverse location on inclined plane body outline when looking up for 60 °.At first sight, seem more complicated, but analyzed that establish a capital really these vanishing point positions is quite simple according to rule 1.For example the vanishing point on the figure (1) is not difficult to find out, it is on the intersection point of 0 ° of parallel (being the horizon) and-45 ° of warps, and this just can judge: this outline line is horizontal line (=0 °), and the azimuth is-45 °; The vanishing point on the figure (2) and for example, can judge equally: this outline line is that the inclination angle is 30 ° a parallax, and the azimuth is 45 °.
Fig. 2, Fig. 3, Fig. 4 is the perspective grid figure that pitch angle is respectively 0 ° (looking squarely), 45 ° (45 ° of elevations angle), 90 ° (90 ° of elevations angle).
Fig. 5, Fig. 6, Fig. 7 is the positive axis survey coordinate diagram that pitch angle is respectively 0 ° (looking squarely), 45 ° (45 ° of elevations angle), 90 ° (90 ° of elevations angle).
Fig. 8, Fig. 9, Figure 10 is the wide-angle perspective coordinate diagram that pitch angle is respectively 0 ° (looking squarely), 45 ° (45 ° of elevations angle), 90 ° (90 ° of elevations angle).
Figure 11 is straightedge body perspective grid figure.
Figure 12 is that straightedge body positive axis is surveyed coordinate diagram.
Figure 13 is a straightedge body wide-angle perspective coordinate diagram.
Figure 14 is the wide-angle perspective phenomenon of the expression space line grid parallel with picture, utilizes this phenomenon, can make the scale on the wide-angle perspective curve ruler.
Figure 15 is the wide-angle perspective curve ruler.
Figure 16 is that a width of cloth is looked squarely ( 0=0 °) perspective view.Because there is the inclined plane in this object, according to rule 4, so what select for use is to look squarely perspective grid figure.Vanishing point from figure (1) as can be seen, it is 60 ° (are because vanishing point on the intersection point of horizon and 60 ° of warps) that there are one group of parallel horizontal line, azimuth in this object the right; From vanishing point (2) as can be seen, there is one group of parallel horizontal line on the left side, and the azimuth is-30 °; From vanishing point (3) as can be seen, one group of parallel parallax is arranged, the inclination angle is 30 °, and the azimuth is-30 ° (are because vanishing point on the intersection point of 30 ° of parallels and-30 ° of warps); From vanishing point (4) as can be seen, one group of parallel parallax is arranged, the inclination angle is-30 °, and the azimuth is-30 °.
Figure 17 is the 30 ° of angle of depression ( 0=-30 °) perspective view (having selected 30 ° of angle of depression perspective grid figure for use).(1) from figure, (2), (3), (4) each vanishing point position as can be seen, the objective position of object is identical among the objective position of this object and Figure 16, just variation has taken place in pitch angle.
Figure 18 is the perspective view (finding out in horizon, 45 ° of angles of depression from horizontal vanishing point position) at 45 ° of angles of depression.Because of this object does not have the inclined plane, according to rule 4, so that select for use is straightedge body perspective grid figure.Vanishing point from figure (1) as can be seen, there is one group of parallel horizontal line on this object the right, the azimuth is 45 °, from vanishing point (2) as can be seen, there is one group of parallel horizontal line on the left side, the azimuth is-45 °, from vanishing point (3) as can be seen, one group of parallel vertical curve (=-90 °) is arranged.
Figure 19 is the positive shaft survey at 45 ° of angles of depression.Because of this object has the inclined plane, according to rule 4, so what select for use is that 45 ° of angle of depression positive axis are surveyed coordinate diagram.Vanishing point from figure (1) as can be seen, there is one group of parallel horizontal line l on this object the right 1, the azimuth is 45 °, and axial rake is 35.3 °, and the axial stretching rate is 0.87; From vanishing point (2) as can be seen, there is one group of parallel horizontal line l on the left side 2, the azimuth is-45 °, and axial rake is 144.7 °, and the axial stretching rate is 0.87; From vanishing point (3) as can be seen, one group of parallel vertical line l is arranged 3, the inclination angle is-90 °, and axial rake is-90 °, and the axial stretching rate is 0.71; From vanishing point (4) as can be seen, one group of parallel parallax l is arranged 4, the inclination angle is 45 °, and the azimuth is-45 °, and axial rake is-60 °, and the axial stretching rate is 0.99; From vanishing point (5) as can be seen, one group of parallel parallax l is arranged 5, the inclination angle is-45 °, and the azimuth is-45 °, and axial rake is-163.7 °, and the axial stretching rate is 0.52.
Figure 20 is the wide-angle perspective figure that a width of cloth is looked squarely.Because of this object does not have the inclined plane, according to rule 4, so what select for use is straightedge body wide-angle perspective coordinate diagram.Vanishing point from figure (1), (2) as can be seen, this object has one group of horizontal line (former line) that is parallel to picture, the azimuth is ± 90 °; From vanishing point (3) as can be seen, one group of horizontal line perpendicular to picture is arranged, the azimuth is 0 °; From vanishing point (4), (5) as can be seen, there is one group of vertical curve (former line) inclination angle that is parallel to picture to be ± 90 °.Can draw from vanishing point (1), (2) and (4), (5) of former line: wide-angle perspective, former line also has vanishing point, and two vanishing points are arranged.Also can draw from figure: in wide-angle perspective, the perspective of straight line has only by principal point O ' and just keeps straight line, and the straight line by principal point produces and becomes Qu Xianxiang, and this just need be described with the wide-angle perspective curve ruler.The ground horizontally-arranged grid of describing from figure is as can be seen: the wide-angle perspective of former line equal segments is five equilibrium not, but littler to the length of picture both sides segmentation, this just need be described with the scale on the wide-angle perspective curve ruler.
Comprehensive the above, the present invention has the number form combination, concept compared with the prior art Clearly, the figure strong sense of reality, drawing technique is grasped easily, simplifies existing scenography, letter Change existing positive shaft survey method, realize the advantage of wide-angle perspective figure method.

Claims (8)

1, a kind of stereoplotter of drawing aphylactic map projection direction perspective view, positive shaft survey, wide-angle perspective figure is characterized in that by some width of cloth horizontal coordinate demonstration perspective grid figure, positive axis in the plane being surveyed coordinate diagram, wide-angle perspective coordinate diagram and a wide-angle perspective curve ruler respectively forms
2, a kind of suitable especially stereoplotter of drawing the perspective view of straightedge body when projecting direction arbitrarily, positive shaft survey, wide-angle perspective figure is characterized in that respectively by a width of cloth horizon, zenith, nadir in the horizontal coordinate being shown that in the plane straightedge body perspective grid figure, straightedge body positive axis survey coordinate diagram, straightedge body wide-angle perspective coordinate diagram and a wide-angle perspective curve ruler and form.
3, by claim 1 and 2 said stereoplotters, it is characterized in that said perspective grid figure and straightedge body perspective grid figure are the gnomonic projection principles in the utilization azimuthal projection, make on paper or flat board.
4, by claim 1 and 2 said stereoplotters, it is characterized in that said positive axis is surveyed coordinate diagram and straightedge body positive axis survey coordinate diagram is the orthogonal projection principle of using in the azimuthal projection, on paper or flat board, make.
5, by claim 1 and 2 said stereoplotters, it is characterized in that said wide-angle perspective coordinate diagram and straightedge body wide-angle perspective coordinate diagram are the equidistant projection's principles in the utilization azimuthal projection, make on paper or flat board.
6, be according to the horizon shape of diaphragm between certain in the said straightedge body wide-angle perspective coordinate diagram by claim 1 and 2 said wide-angle perspective curve rulers, make with transparent plate.
7,, it is characterized in that all having on said each width of cloth coordinate diagram plane polar coordinates to show by the said stereoplotter of claim 1 to 5.
8, by claim 1,2 and 6 said stereoplotters, it is characterized in that said wide-angle perspective curve ruler is graduated.
CN 85107564 1985-10-10 1985-10-10 The stereoplotter of aphylactic map projection direction Pending CN85107564A (en)

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105329032A (en) * 2015-12-01 2016-02-17 唐文虎 Sphere illustrative diagram, composition method of North Pole position thereof and used template
CN108445781A (en) * 2018-01-26 2018-08-24 北京金橙子科技股份有限公司 Rotate marking processing method and system
CN112644209A (en) * 2020-12-24 2021-04-13 丽水市左尚设计装饰工程有限公司 Auxiliary system for computer graphic design
CN114252063A (en) * 2021-12-22 2022-03-29 内蒙古工业大学 Ancient building surveying and mapping device based on geometric perspective method and surveying and mapping method thereof

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105329032A (en) * 2015-12-01 2016-02-17 唐文虎 Sphere illustrative diagram, composition method of North Pole position thereof and used template
CN108445781A (en) * 2018-01-26 2018-08-24 北京金橙子科技股份有限公司 Rotate marking processing method and system
CN108445781B (en) * 2018-01-26 2021-03-19 北京金橙子科技股份有限公司 Rotary marking processing method and system
CN112644209A (en) * 2020-12-24 2021-04-13 丽水市左尚设计装饰工程有限公司 Auxiliary system for computer graphic design
CN114252063A (en) * 2021-12-22 2022-03-29 内蒙古工业大学 Ancient building surveying and mapping device based on geometric perspective method and surveying and mapping method thereof

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