GB2203998A

GB2203998A - Drawing instrument

Info

Publication number: GB2203998A
Application number: GB08707092A
Authority: GB
Inventors: William Cochrane
Original assignee: Individual
Current assignee: Individual
Priority date: 1987-03-25
Filing date: 1987-03-25
Publication date: 1988-11-02
Anticipated expiration: 2007-03-25
Also published as: GB2203998B; WO1990003278A1; GB8707092D0

Abstract

A drawing instrument is in the form of a set square (12) having a first straight edge (13) associated with a graduated scale (14) and a representation of a curve (15) which when the square is shifted so that a point marked adjacent the edge (13) is intercepted by the curve (15), the straight edge intercepts a projection line at a point enabling a dimension measured along the scale (14) to be accurately projected on to the projection line.

Description

"DRAWING INSTRUMENT" This invention relates to a drawing instrument and in particular to an instrument for facilitating the drawing of accurately dimensioned angular perspective projections.

Present methods of accurately dimensioning angular perspective projections are time consuming or inaccurate or both. It is known to employ a method known as the method of measuring points wherein a measurement along a ground line may with the aid of a special projection line to a point on a horizon line, spaced from a vanishing point by the same distance as the vanishing point is spaced from a datum point in the ground line, be used to project a measurement on the ground line to a line between the ground point and the vanishing point. However, this method is inconvenient, requiring a multiplicity of steps, and is limited by the available extent of the ground line and the requirement of a varnishing point on the drawing paper.One object of the invention is to provide an instrument which is based on the method of measuring points but simplifies the process of construction.

According to one aspect of the invention, a drawing instrument comprises means for defining a straight line and enabling marking of intercepts therewith, means for enabling measurements along an axis parallel to said line, the instrument enabling translation of the said line along a second axis perpendicular thereto, and means for defining a curve in the plane of said axes such that graphical intercepts with said curve may be observed, the curve having the form x = Ay/(B + y) ) + C, wherein A, B and C are constants, y is a coordinate along the said first axis and x is a coordinate along the second axis.

Preferably the instrument is in the form of a set square having one edge defining said straight line and associated with a graduated scale, a second edge at right angles to the first enabling the translational movement of the straight line. The set square may be transparent and bear the said curve as a line marked thereon, such as by engraving. However, other embodiments, such as defining the curve as an edge, are also possible.

According to another aspect of the invention, a drawing instrument comprises a straight edge associated with a graduated scale, extending in a first direction, and a marker line, with which intercepts by graphical lines may be detected, the marker line representing the locus of a point of which a coordinate along a first axis parallel to said first direction represents a selectable distance from a datum and of which a second coordinate represents a distance along a second axis, perpendicular to the first axis, identifying the intersection of a first notional line extending from a point spaced by the selected distance from the datum along the second axis and a selectable point on a second notional line parallel to the second axis and a third notional line extending from the datum to a selectable vanishing point, the distance between the datum and the vanishing point being the same as the distance between the vanishing point and the said point on the said second line, the instrument having means, such as a straight edge, defining translational movement of the instrument in a direction parallel to the second axis.

There follows a description of an embodiment of the invention with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is an explanatory diagram showing a method of projecting dimensions on to construction lines in angular perspective; Figure 2 illustrates one embodiment of the invention and a first stage in a preferred manner of use thereof; and Figure 3 illustrates the embodiment of the invention in a second stage of use.

Before an embodiment of the invention is described, it is convenient to refer to Figure 1 which illustrates an example of transferring a dimension accurately to a projection line in angular perspective.

In Figure 1, the point C is the centre of vision, the point G, which is spaced by a distance d from the point C, is termed the ground point and a point V is a selectable vanishing point used for the construction of perspective lines. In order to represent a dimension accurately in angular perspective on a line GV, it is first necessary to construct a measuring point, M, such that it lies in the horizon line which passes through the points C and V such that the distance VM is equal to the distance VG. This normally requires the use of a pair of compasses or dividers.

Let it be assumed that one wishes to transfer a dimension, of n units to the line GV. A point N in the ground line is selected such that GN represents the desired dimension. A line MN is drawn from the measuring point to the point N in the ground line.

The point of intersection of the line MN with the line VG, namely the point R, is the true projection in angular perspective of line in VG and n units long.

The method of measuring points is fairly slow and inconvenient especially if there is a multiplicity of projection lines and a multiplicity of dimensions which are required to be projected thereon.

The preferred embodiment of the invention effectively reduces the aforementioned method to, effectively, a single action; in particular it eliminates the necessity of constructing the point M and the line MN.

Before the preferred embodiment of the invention is described, it is convenient to refer- to the other features in Figure 1, wherein the angle a is the angle between CG and the projection line GV, P is a point of which the x-coordinate, that is to say the coordinate along the axis coincident with or parallel to the ground line and the y-coordinate GQ is of the same magnitude as the distance GN.

In Figure 1, VM = VG = d cosec a, where d is the distance between the centre of vision C and the vanishing point V and a is the angle made between CG and the projection line VG. It is convenient to define the Cartesian coordinates of various points as follows: G = (o,o) C = (o, d cotan a) V = (d, d cotan a) M = (d-d cosec a, d cotan a ) If N is a point on the x-axis (the ground line) with coordinates (n,o) the equation of line MN is given by: y = (d cotan a) [(x-n)/(d-d cosec The equation of the line VG is:: y = x cotan a ................... (2) It may be shown that at the intersection R, the x-coordinate is given by x=dn/(d cosec a + n) (3) In order that measurements may be related to the vertical (CG) one may define a point P coordinate (dn/(d cosec a + n), n] It follows (by substitution for n) that the locus S of the point P is x = dy/(d cosec a + y)................. (4) This, since a is selectable and, as will be seen, the selection of an origin is arbitrary may be presented in the form x = Ay/(B + y)+C ........................ (5) where A, B and C are constants.

Having regard to Figure 1, a preferred embodiment of- the invention requires some means for defining a straight line extending in a direction parallel to the y axis (GQ) which can be shifted or translated in the x direction, that is to say an axis parallel to the ground line, a scale extending in the y direction, so that the dimension of which the projection is to be made can be measured, and means for defining the locus S in a manner which enables the construction of the point R by means of (a) marking of the point Q and (b) the lateral shift by the distance QP of the straight line.

Figure 2 illustrates one embodiment of the invention at the first phase of its use. In Figure 2 is shown a drawing easel 10 having a T-square 11 disposed in customary fashion thereon. Already drawn on paper on the easel is a ground point G with two projection lines GY and GZ. A set square 12, constituting an embodiment of the invention, is supported by the T-square for translational movement in the horizontal direction extending through the point G. The use of a T-square 11 is not essential and the set square could be mounted for the horizontal translational movement by some other means if desired.

The set square 12 has a straight edge 13 extending in the "vertical" direction and associated with a graduated scale 14. Marked on the set square, preferably by means of engraving, is a curve 15 conforming to equation (4) wherein d, in this particular embodiment is 50 centimeters, and the angle a is, in this particular embodiment, 450.

Initially the instrument 12 is positioned so that the straight edge 13 is spaced from a vertical line through the point G by the distance along the ground line of the line 15 and the straight edge 13.

In the present embodiment, this corresponds to the maximum width of the set square. For convenience also the distance between the intercept of the curve 15 with the ground line and the intercept of the straight edge 13 with the ground line is marked on the T-square with a line shown as 0/50, representing measurements in the range 0 to 50 centimeters.

Let it be supposed that the desired measurement is 18 centimeters. A mark 1 is made closely adjacent to the straight edge 13 at the position corresponding to 18 centimeters from the ground line. Then, as shown in Figure 3, the instrument 12 is translated along the ground line, that is to say in the direction perpendicular to the direction in which the straight edge 13 extends, until the point 1 intercepts the line 15. The intersection, shown at point 2, of the edge 13 with the line GY corresponds to the perspective projection of the distance 18 centimeters on to the line GY. Also, the point 3 has the same vertical displacement from the ground line as has the point 2.To locate a corresponding point on the construction line GZ, it is only necessary to shift the leading edge to the point 3 which ispaced from the vertical line through G by the same distance as the point 2 is spaced from that line. This may be done using a graduated scale on the T-square as shown.

Thus, a true dimension in a reference, preferably vertical, direction may be projected on to an oblique construction line to provide in angular perspective a true representation of that dimension.

The first curve 15 on the instrument may be used to the full extent of the vertical scale, that is to say to make perspective projections or dimensions up to 50 centimeters. A second curve 16 is marked on the instrument to enable dimensions of between 50 and 100 centimeters to be projected. The curve 16 is drawn for a value of d equal to 100 centimeters and when using the curve 16 it is necessary to place the edge 13 so that its distance from the vertical through the ground point G is equal to the sum of the distances, along the ground line, of the curves 15 and 16. For convenience, the sum of these distances may be marked on the T-square 11.

The instrument is simple and convenient to use in the form shown in Figures 2 and 3, but more sophisticated embodiments are possible. For example, means carried on a slider movable lengthwise of the scale 14 may be provided for marking the point 1 and, as indicated previously, some mechanical means may be provided for traversing the instrument to provide the shift required for detecting the intercept of that point with the curve 15 or the curve 16.

Claims

CLAIMS:

1. A drawing instrument comprising means (13) for defining a straight line and enabling marking of intercepts therewith, means (14) for enabling measurements along an axis parallel to said line, the instrument enabling translation of the said line along a second axis perpendicular thereto, and means (15) for -defining a curve in the plane of said axes such that graphical intercepts with said curve may be observed, the curve having the form x = Ay/(B + y) + C, wherein A, B and C are constants, y is a coordinate along the said first axis and x is a coordinate along the second axis.

2. An instrument according to claim 1 wherein the means (13) defining the straight line comprises a straight edge having a graduated scale (14) associated therewith.

3. An instrument according to claim 2, in the form of a set square having a transparent portion on which the said curve is marked.

4. A drawing instrument comprising a straight edge (13) associated with a graduated scale (14), extending in a first direction, and a marker line (15), with which intercepts by graphical lines may be detected, the marker line representing the locus (S) of a point (P) of which a coordinate along a first axis (y) parallel to said first direction represents a selectable distance (n) from a datum and of which a second coordinate represents a distance along a second axis (x), perpendicular to the first axis, identifying the intersection (R) of a first notional line extending from a point (N) spaced by the selected distance from the datum along the second axis and a point (M) on a second notional line parallel to the second axis and a third notional line extending from the datum (GV) to a vanishing point, the distance (GV) between the datum and the vanishing point being the same as the distance (MV) between the vanishing point and the said point on the said second line, the instrument having means for defining translational movement of the instrument in a direction parallel to the second axis.

5. A drawing instrument according to claim 4, in the form of a set square having an edge at right angles to the first edge and for enabling translation of the set square in the direction parallel to the second axis.