A SOFTWARE CODE FOR DESIGN AND SIMULATION OF SUN DIALS
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1 MONCLASSICO 30 maggio - 1 giugno 2008 A SOFTWARE CODE FOR DESIGN AND SIMULATION OF SUN DIALS Gianpiero Casalegno giancasalegno@yahoo.it
2 Program features Operating System : XP / 2000 / Vista (WINE compatible) directional and azimuth dials hour lines and day lines design graph export to vector / raster file shadow simulation reverse engineering of existing dials freeware
3 User interface menu tool bar graph area mouse real coordinates dial frame dimensions
4 Definition of a new dial : type family : directional azimuth local time GMT GMT +n GMT -n
5 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
6 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
7 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
8 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
9 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
10 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
11 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic vertical declininganalemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
12 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
13 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
14 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
15 Dial types directional : inclined declining vertical declining horizontal polar equatorial azimuth : horizontal analemmatic verticale declining analemmatic horizontal ortographic projective vertical declining ortographic projective horizontal stereographic projective vertical declining stereographic projective
16 New dial definition : coordinates all earth latitudes editable data base
17 New dial definition : dial frame declination inclination orthostyle length dimension orthostyle position
18 New dial definition : options day lines hour lines analemma other options
19 Hour line types astronomical (french) italic and babilonic da campanile and twilight temporal
20 New dial definition : background image pre-view selected file reference opzioni varie points real distance orthostyle position
21 Positioning and dimensioning
22 Compute shadow of obstacles
23 Existing dials simulation
24 View : tables
25 View : tables
26 View : style parameters
27 View : lighting conditions
28 View : lighting conditions light off: 21/6 14:45 light on : 21/6 5:20 light off : 21/3 16:05 light on: 21/3 sunrise light on : 21/12 sunrise light off : 21/12 sunset
29 View : lighting conditions
30 Print, save,, export copy graphs and tables to the clipboard print report with selected graphs and tables export to DXF vector file export to JPG, TIF, GIF, PCX, BMP raster file 1:1 multipages print
31 1:1 multipages print
32 Help
33 Wall declination Based on the shadow/wall angle compute sun parameters and wall declination put the result into the actual project
34 Wall declination
35 Shadow simulation and sun parameters computation simulation of any sun dial type (directional, azimuth) simulation time : current, manually set or dinamically changed (date / time) main sun parameters computation (declination, azimuth, height ) current time shown for any time measurement system show sunrise, sunset, local noon, twilight
36 Shadow simulation and sun parameters computation
37 Screen Saver based on any sundial you designed with the program
38 Reverse engineering Problem given an old dial with only some elements left (lines, points, style ) compute the original design parameters (latitude, declination, style )
39 Reverse engineering Classical approach For any particular situation : measure an element and then find the unknowns by means of trigonometric relationships. ex. equinox line is available => measure angle, find declination Disadvantages: huge number of possible situations, a program can not cover them all program would be a long list of commands, one for each situation / unknown
40 Reverse engineering Innovative approach Consider the problem as a data fitting situation : given a list of measured values, find the parameters of the given model that best match measurements ex. linear regression Y = a * X + b Given measurements (X i,y i ) find parameters a and b that best approximate the results.
41 Reverse engineering ex. declining vertical dial showing local time X i = X (ω, δ, φ, d, λ, x, y) X i X Y i = Y (ω, δ, φ, d, λ, x, y) ω = known hour angle δ = known sun declination φ = latitude d = wall declination λ = orthostyle length x,y = orthostyle base coordinates Y Y i P i
42 Reverse engineering 1. measure the position of N points (with known ω e δ) 2. make a system of 2*N non-linear equations with 5 unknowns f i (φ, d, λ, x, y) = k i i = 1 2N where k i are the measured coordinates of N points. 3. solve the system and find the 5 unknown parameters
43 Reverse engineering Levenberg-Marquardt algorithm Consider the cost function F ( ϕ, d, λ, x, y)= = ( ( ) ) 2 f = iϕ d, λ, x, y ki i= 1, ε i= 1 2 i equal to the sum of squares of residual errors between model and measurements. The algorithm will look for a minimum of F through an iterative process that should converge to the local minimum nearest to the initial starting hypothesis.
44 Reverse engineering list of measured points list of measure lines ricerca find a soluzione solution save / open input data soluzione solution
45 Reverse engineering : input of measured lines and points line type hour point coordinates (min. 2) point type point coordinate hour
46 Reverse engineering ex. italic hour dial, three hour lines known recovered dial :
47 Reverse engineering ex. italic hour dial, three points known (intersection between hour lines and equinox line) recovered dial :
48 Reverse engineering ex. italic hour dial, three points known (intersection between hour lines and day lines) recovered dial :
49 Reverse engineering ex. italic hour dial results : unknown true value case 1 case 2 case 3 φ d λ x y
50 Reverse engineering ex. italic dial ±1 cm error : in the presence of errors use as many data as possible recovered dial :
51 Reverse engineering ex. temporal hour dial, three points known (intersection between hour lines and equinox line) recovered dial :
52 Reverse engineering Measured elements must allow the identification of one and only one dial. ex. left: italic dial with three hour lines / day lines intersections known, right : recovered dial => more than one solution exist starting dial recovered dial
53 Reverse engineering Measured elements must allow the identification of one and only one dial. ex. left : temporal dial with three hour lines known, right : recovered dial => more than one solution exist starting dial recovered dial
54 Reverse engineering Measured elements must allow the identification of one and only one dial. ex. left : babilonic dial with three meridian / hour lines intersections, right : recovered dial => more than one solution exist starting dial recovered dial
55 Reverse engineering For good solutions it is advisable to : intrduce the larger possible number of input data use points instead of lines (as long as possible) try a local search starting from good starting values freeze known values search around the starting values freeze the value
56 Reverse engineering previous ex. (italic dial with three hour lines / day lines intersections known) : when the style position is known and introduced ( frozen ) we obtain the correct result wrong good
57 Reverse engineering previous ex. (babilonic dial with three meridian / hour lines intersections known) : when the style position is known and introduced ( frozen ) we obtain the correct result wrong good
58 Future enhancements New types of dials : sheppard cylindrical dial Joël Robic s cylindrical dial height dials reflection (mirror) dials bifilar dials
59 Future enhancements Various : day lines for 12 months (azimuth dials) style position for 12 months (analemmatic dials) quarter of hour lines user preferences (line thickness, colour etc.) user interface and help files translated to new languages
60 Download, comments, suggestions, bugs
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