<content> Drawing text </content>

48879e23-eff7-4188-af2d-b776ccd97aa3 65 overlord 4 5 false false 0 10 decimal

&[DATE] &[TIME] - &[FILENAME]

<content> Drawing text </content> <content> Fonts </content>

Fonts

These two fonts are from "Creating amazing images with Mathcad", by Byrge Birkeland.

~Φ00 0022001 - 1 - 0025 mat 0.5 0.5 0.5 1 NaN * 0110001002299222000000039 mat 011001 NaN * 2332266886066886211 mat 00000000000233445775445754433200233201 NaN * 455441 NaN * 332232001 - 1 - 002355877991010997644122012341058765100000101001 - 0100000101001 - 00010100001010339 mat 018701 NaN * 6661 NaN * 5.5 6.5 6.5 5.5 5.5 1 NaN * 2221 NaN * 1.5 2.5 2.5 1.5 1.5 00990004001133105950668860000002200202000220020200325 mat 0023 4.2 577 5.3333 4.8 77 4.4 2.8 511 1.8 01 NaN * 1123 3.8 2.2 11 NaN * 22 2.4 423200 1.2 0011 1.8 45 2.4 4.8 776 4.8 303211 1.8 4.2 3076 5.4 77010000000000002000000100000000020333 mat 0 0.5 1004466425 mat 0233223320002 - 2 - 1 - 09101111901001 - 01 - 00101311 mat 013310011002 - 2 - 09111110901 - 2 - 0101001 - 01 - 00311 mat 0 2.5 2.5 3.5 3.5 66 3.75 66 3.5 3.5 2.5 2.5 00 2.25 001 2.6667 00 2.6667 12 3.5 56 4.3333 77 4.3333 65 3.5 21219 mat 23355332200221133446644331213 mat 0.5 110 0.5 0 0.5 0 0.5 - 03 - 01 - 1035 mat 033003344325 mat 0.5 0.5 0.5 01022033 mat 013200099025 mat 0257752001 NaN * 2234554322002799720278872112101010100001 - 01 - 01 - 01 - 0319 mat 244201220099778028 mat 07722357752023455420000113446799778876553000001 - 01010101 - 01 - 01 - 0100321 mat 02577 5.5 7752023455422455432020023 4.5 67997788765544321122101011010101 - 01 - 01 - 0001 - 01 - 01 - 00326 mat 4667766300441 NaN * 144 3.5 1100445599644005588 5.5 5219 mat 0257753227700234554320200246658899445542112210101010000001 - 01 - 01 - 01 - 00322 mat 025775322345752001 NaN * 234554322200246657887799720211245542101010101 - 01 - 0101000101010100327 mat 1377002255100699778860211 mat 025775522001 NaN * 2345543221 NaN * 2345543222002359953202112 3.5 4.5 4.5 3.5 20 6.5 5.5 5.5 6.5 7887 6.6 1010120210001010101000101010100331 mat 025775200245543201 NaN * 2345543222002799753342112205445788751010101010101 - 01 - 000101010100327 mat 0.5 0.5 0.5 1 NaN * 0.5 0.5 0.5 0100565220022037 mat 0.5 110 0.5 1 NaN * 0.5 0.5 0.5 0 0.5 0 0.5 - 005653 - 01 - 10022039 mat 0077 1.5 770 3.5 2.5 01356 3.5 28 mat 066001 NaN * 0660022332044554211 mat 07700 5.5 000 2.5 3.5 6531028 mat 3.5 3.5 3.5 1 NaN * 3445520234433010022459977886522200001 - 20121 - 02 - 100317 mat 0255211256655432234557752001 NaN * 3443320011278874467763223 2.5 2.5 799720 3.5 3.5 5.5 5.5 3.5 10201 - 01 - 01 - 02 - 0101010101010100020200333 mat 02 2.67 5.33 674301 NaN * 354300220099003363214 mat 0577 5.5 775001 NaN * 22455421 NaN * 22455420023 4.5 67990014432110588765501011010000001 - 01 - 000001 - 01 - 00326 mat 25754322345752002002211278877997200101 - 01 - 01 - 01 - 0101010317 mat 05775001 NaN * 224554200279900188721101010000001 - 01 - 00315 mat 07722442277000011445588990213 mat 0224422770000445588990211 mat 25774455432234575200200244332112788779972001000001 - 01 - 01 - 01 - 0101010321 mat 02255775522000044009955990213 mat 022000099025 mat 02577554320200299211221010001 - 01 - 00311 mat 02257 3.5 75220000400 4.5 995990212 mat 0772200001199027 mat 02246688642000063600996990213 mat 0226886620000700992990211 mat 0257752001 NaN * 2234554322002799720278872112101010100001 - 01 - 01 - 01 - 0319 mat 0225775001 NaN * 2245542004467990058876550001010000001 - 01 - 00317 mat 0246642001 NaN * 224421 NaN * 5.4142 677 5.7321 5.4142 2002799720277220 0.5858 0011 0.5858 101010100002 - 02 - 00000000322 mat 0223575775001 NaN * 2245542004400467990058876550000001010000001 - 01 - 00320 mat 025776322345752002455432020024556788779976443211221010101 - 01 - 01 - 01010101 - 01 - 01 - 00325 mat 2.5 4.5 4.5 7700 2.5 2.5 00889988029 mat 0025775543220920029921129901010001 - 01 - 000313 mat 347642030099399028 mat 034689121197642090060099399399214 mat 02 3.5 57 4.5 75 3.5 20 2.5 000 2.7 00 4.5 99 6.3 99 4.5 0213 mat 0 2.5 2.5 4.5 4.5 764209500599699210 mat 0772770050000118998810211 mat 0332233002 - 2 - 1 - 1 - 101011112 - 29 mat 671060099025 mat 0033001101 - 2 - 2 - 111110101 - 1 - 29 mat 0244200686797627 mat 07700001 - 1 - 025 mat 023109669925 mat 66443200234461 NaN * 422440665664200100022442000101010100002 - 02 - 00319 mat 66432200223461 NaN * 422442466599001002022442010100000101002 - 02 - 00319 mat 64200246422464664200222444101010102 - 02 - 00313 mat 66443200234461 NaN * 422440995664200100022442000101010100002 - 02 - 00319 mat 66420024642261 NaN * 424346642002223304440101010102 - 000002 - 0317 mat 3344335643110011303344777997443300000002 - 01010000000317 mat 64432002344321024661 NaN * 4224466566420011 - 2 - 2 - 1 - 1 - 3 - 3 - 1 - 602244200101010101 - 01 - 01010002 - 02 - 00325 mat 664322002244604665990044000101000002 - 000313 mat 022001 NaN * 11100660079700000022039 mat 001331101 NaN * 2221 - 2 - 2 - 06601 - 07970010001 - 00220312 mat 02246 3.33 4.67 3.33 2200003004664990212 mat 022000099025 mat 0224455778876543220000440044005665665660002 - 0002 - 0001011010000320 mat 02244664322000044004665660002 - 0001010000313 mat 2466420021 NaN * 4224400246642002244201010101002 - 02 - 00315 mat 02234664322001 NaN * 422443 - 3 - 10024665663 - 022442001010101000002 - 02 - 00319 mat 64432002344661 NaN * 4224466566420013 - 3 - 6022442001010101000002 - 02 - 00319 mat 02234 4.5 643220000455 4.866 4665660001 - 0 0.1667 - 2.6667 1010000313 mat 0 1.5 4.5 66 4.5 2.75 2.75 3.5 46 4.5 1.5 00 1.5 3.25 3.25 2.5 20 1.5 00 1.5 2 3.5 3.5 55 4.5 4.5 66 4.5 4 2.5 2.5 11 1.5 1.5 1010102 - 01 - 01010102 - 01 - 00321 mat 311001134653355339966552002225566900000010102 - 000000317 mat 664422002344606622662001000002 - 000101000313 mat 354320230663660028 mat 6876543202345606636636600300214 mat 01 2.5 46 3.5 543202000 2.25 00 3.75 66 4.5 66300000000000000313 mat 1365 3.5 20213 - 3 - 66 1.5 6603 - 00000000039 mat 0662660040000115665510211 mat 1243323342110111 - 2 - 2 - 1 - 3.5 4.5 5.5 10111110 5.5 4.5 3.5 1 - 101 - 01101 - 0101 - 1 - 00315 mat 011000099025 mat 0233433201121102 - 2 - 1 - 3.5 4.5 5.5 10111110 5.5 4.5 3.5 1 - 2 - 0101 - 1 - 0101 - 01101 - 0315 mat 941 mat :

~Φ01 020022 mat 001 NaN * 000 0.5 01825 mat 001 NaN * 116806825 mat 021 NaN * 241 NaN * 0.25 3.25 1 NaN * 0.75 3.75 08008033055211 mat 012211231 NaN * 1.5 1.5 2113355400610202 - 01 - 0000311 mat 202301 NaN * 22255560002022000022039 mat 3321002003210012554001 - 01 - 002000310 mat 004 2.5 22 mat 0071 - 0.25 032 mat 0071 - 0.25 - 032 mat 1.5 1.5 1 NaN * 031 NaN * 300401301328 mat 111 NaN * 021302225 mat 0.5 11011 - 0.5 - 0.5 0.5 0.5 1022035 mat 022222 mat 0.5 0.5 0.5 01022033 mat 020422 mat 03300 1.5 1.5 4.5 4.5 1.5 2020035 mat 0.75 0.75 006 5.25 23 mat 300 1.5 33000 0.75 2.25 3.75 4.5 4.5 001 - 102037 mat 033 1.5 0.75 30 1.5 1.5 2.25 3.75 3.75 66201000037 mat 2.25 2.25 0306 2.25 2.25 24 mat 033003 1.5 1.5 336620200036 mat 300330 4.5 4.5 1.5 1.5 2.25 2.25 20202036 mat 0300066 5.25 24 mat 1.5 1.5 1.5 1.5 1.5 0363022 - 2 - 2035 mat 300330 3.75 3.75 4.5 4.5 1.5 1.5 2 - 02 - 02 - 036 mat 0.5 0.5 0.5 1 NaN * 0.5 0.5 0.5 0100343220022037 mat 0.5 11011 NaN * 0.5 0.5 0.5 1 - 0.5 - 0.5 0.5 0.5 034310220022039 mat 20212323 mat 021 NaN * 02 1.5 1.5 0 2.5 2.5 25 mat 02012323 mat 1.5 1.5 1.5 1 NaN * 1.5 1.5 00 0.5 0013 4.5 220003037 mat 31133440021122002211 - 2 - 02 - 0202010310 mat 0 1.5 31 NaN * 0.375 2.625 0600 1.5 1.5 26 mat 0 1.5 1.5 0 1.5 1.5 00003336600200200038 mat 3003 4.5 4.5 1.5 1.5 202034 mat 0 1.5 33 1.5 0000 1.5 4.5 660010100037 mat 30031 NaN * 0 1.5 006603327 mat 0031 NaN * 0 1.5 06603326 mat 30033 1.5 4.5 4.5 1.5 1.5 3320200036 mat 001 NaN * 331 NaN * 030600603328 mat 000622 mat 033 1.5 1.5 620033 mat 001 NaN * 30306003626 mat 00360023 mat 00 1.5 330636025 mat 0033060624 mat 03300 1.5 1.5 4.5 4.5 1.5 2020035 mat 0 1.5 1.5 00336600200035 mat 033001 NaN * 2.25 3 3.75 1.5 1.5 4.5 4.5 1.5 0 0.75 0020200000039 mat 0 1.5 1.5 001 NaN * 1.5 3336600300200000038 mat 0 1.5 3 1.5 3 4.5 33 - 033 mat 1.5 1.5 1 NaN * 030606625 mat 00336 1.5 1.5 6020034 mat 0 1.5 360623 mat 0 0.75 1.5 2.25 36060625 mat 031 NaN * 030606025 mat 0 1.5 1.5 1 NaN * 1.5 363003626 mat 0303660024 mat 10011 - 1 - 7724 mat 024022 mat 01101 - 1 - 7724 mat 01234323 mat 02 0.5 - 0.5 - 22 mat 010022 mat 2201 NaN * 2120330221020003037 mat 02201 NaN * 001133006202000037 mat 20023311202034 mat 20021 NaN * 223311060202000037 mat 02200222331100202036 mat 2111 NaN * 02 5.5 5.5 004420000036 mat 20021 NaN * 022331101 - 1 - 42020020038 mat 001 NaN * 22006003300002036 mat 0011 NaN * 004 0.5 0.5 05602000036 mat 0111 NaN * 11 1.5 - 1.5 - 405620000036 mat 001 NaN * 20206002426 mat 0016 0.5 0.5 02033 mat 001 NaN * 44201 NaN * 2204003330030000220000310 mat 001 NaN * 22004003300002036 mat 02200113312020035 mat 001 NaN * 02202 - 401133000202037 mat 221 NaN * 20022 - 403311000202037 mat 001 NaN * 20040330002035 mat 01212333 - 033 mat 2111 NaN * 02 0.5 0.5 60442 - 0000036 mat 221 NaN * 2004001140002 - 0136 mat 01240423 mat 012344040425 mat 021 NaN * 020404025 mat 011 NaN * 0.5 24002 - 425 mat 0202440024 mat 1 0.5 0.5 0 0.5 0.5 1 0.5 - 0 2.5 3 3.5 6 6.5 27 mat 000622 mat 0 0.5 0.5 1 0.5 0.5 0 0.5 - 0 2.5 3 3.5 6 6.5 27 mat 941 mat :

~Φ00 4 el 12 2.2778 4.2778 45 5.2778 77 5.3889 5.6111 77 5.7222 600 2.5 2.5 00 2.5 2.5 3.5 3.5 5.5 5.5 6.5 6.5 9215 mat :

~Φ00 4 el ~Φ00 4 el 5 4.7222 2.7222 32 1.7222 00 1.6111 1.3889 00 1.2778 11 NaN * 2.3889 4.3889 4.6111 2.6111 2.3889 9 6.5 6.5 99 6.5 6.5 5.5 5.5 3.5 3.5 2.5 2.5 00 3.5 3.5 5.5 5.5 3.5 220 mat augment :

~Φ_Str_1_!"#$%&'()*+,-./0123456789:;<=>?@ :

~Φ_Str_2 ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_` :

~Φ_Str_3 abcdefghijklmnopqrstuvwxyz{|} :

~Φ00 ~Φ00 ~Φ_Str_1 ~Φ_Str_2 ~Φ_Str_3 concat stack :

~Φ01 ~Φ01 ~Φ_Str_1 ~Φ_Str_2 ~Φ_Str_3 concat stack :

<content> Chars </content>

Drawing Characters

Let's try to draw an O given it's xy coordinates and convering them into a complex vector. We go to use this auxiliary function

Z ReIm Z Re vectorize Z Im vectorize augment eval 11 line :

Now, we want the same letter but with curved borders.
np is the number of points pr. unit length of the arc.

M np txtChar Z M 1 row i M 2 row * + transpose eval : M rows 2 ≡ Z S 01 matrix : c 1 M cols 1 - (range M 3 c el 0 ≡ S S Z c el Z c 1 + el stack eval : v 0.25 M 3 c el * π * : R 12 v sin * / : H 1 i v cot * + 2 / : 13 mat m Z c 1 + el Z c el - abs np * 2 v * R * abs * Floor 1 + : t π 2 / v - 2 v * m / 0 m range * + : S S Z c el Z c 1 + el Z c el - (H R e i t *^* vectorize - (* + stack eval : 41 line if for S 31 line if 21 line :

Convert xy pairs into complexes.

If there are not arcs, that's all.

Not an arc, just draw a line between Zc+1 and Zc

Number of points (m+1)

Range variable

Draw an arc
between Zc+1 and Zc

We define NaN as a big number, and cycle colors (Ber idea) and try to emulate the halts.

Z C txtNaN r 1 Z length range : C 0 > A Z abs 0.001 NaN * ≥ vectorize r el r augment eval : A Z abs 0.001 NaN * < vectorize r el r augment eval : if f A 11 findrows : (0 ≠ f 2 col eval 0 if 31 line :

If C ...

Locate where are NaN's

Locate where are not NaN's

S txtPlot P 0 : r 0 : 12 mat f S 1 txtNaN : (0 ≡ P S ReIm 11 sys : f 0 f S length 1 + stack eval : k 2 f length range Z S f k 1 - el 1 + (f k el 1 - (range el : Z normi 0.001 NaN * > continue P r r 1 + : el Z ReIm : k f length ≡ continue j 1 CycleColors range P r r 1 + : el : for if 21 line if 21 line for P mat2sys.1 31 line if 21 line :

Locate NaN's

If there are not one, returns real and imag parts. That's all.

Discard NaN's

If there are two consecutive NaN, discard Z

Acept Z

Cycle colors as Ber procedure, only if isn't at the end.

Using

NaN 1000000 :

CycleColors 5 :

<content> Words </content>

Drawing Words

For draw words we use following parameters:

s text

ap = x+i*y anchor point of the text
it italicization factor
sp space between the characters
wh = wi+i*he wi: width relative to the font's default
he height relative to the font's default
aa = ha+i*va ha: horizontal alignment: 0 is left, 1 is center and 2 is right
va: vertical alignment: 0 is bottom, 1 is center and 2 is top
an angle between the positive x axis and the base line of the text

sc character scaling factor
np number of points pr. unit length of the arc
fo font with char matrices and avaible strings

cc control characters for sub, superscript and new line (not implemented yet)

Z txtΔz W Z Z 0 txtNaN el eval : R I 12 mat W Re vectorize W Im vectorize 12 mat eval : R max R min - i I max I min - (* + eval 31 line :

With and Heigth of a vector of complexes discarding the NaN's

P Q txtStack P NaN ≡ Q P P P length el Q 1 el - abs TOL < Q 2 Q length range el NaN Q stack if stack if 11 line :

Discard P if it is NaN

Discard first point in Q if it is close to last in P, and draw constinously or ...

Halt with a NaN between P and Q.

TOL 105 -^:

Defalut value for assume that two points are the same.

s ap it sp wh aa an sc N fo cc txtWord zo 0 : r 0 : Z NaN : v 0 : 14 mat wo sc fo 1 el N txtChar * txtΔz Re eval : k 1 s strlen range f fo fo length el s k 1 substr findstr : f 1 - ≠ char sc fo f 1 el (el N txtChar * eval : Z Z char zo + txtStack eval : zo zo sp + char txtΔz Re + eval : 31 line zo zo sp + wo + eval : if 21 line for Z Z 0.5 it * i * Z Z Conjugate - (* - eval : Z 0.5 Z wh Re wh Im + (* Z Conjugate wh Re wh Im - (* + (* eval : Δz 0.5 Z txtΔz * : Z Z aa Re Δz Re * - i aa Im * Δz Im * - eval : ap e i an *^Z * + eval 81 line :

With for blanks

Draw each char

Update displacements

Italics

wi & he relatives factors

Alignments

Rotate and trasnlate

Normal text

s fo Word s 0011 i + i 014 fo 0 txtWord 11 line :

Italics

s it fo Word s 0 it 11 i + i 014 fo 0 txtWord 11 line :

Rotated

s ap an fo Word s ap 0.4 11 i + i an 14 fo 0 txtWord 11 line :

Animating the view point

Animating an azimut-elevation matrix simulating 3D views in a 2D plot.

α ε pView2 α cos ε sin α sin * - α sin ε sin α cos * 0 ε cos 32 mat :

a γ axis ax 63 matrix : Id 3 identity : 12 mat ax 2101813 mat el a : (γ * a Id * γ * x y z stack augment 21 sys 21 line :

γ 30 ° * 30 ° * pView2 :

α σ 0.9 α cos abs * 0.3 + :

α Anim α 30 ° * pView2 az: X°, el: 30° X α deg / 0 var2str strrep 12 mat α 360 ° * < 30 ° * α 360 ° * - pView2 az: 30°, el: X° X α 360 ° * - deg / 0 var2str strrep 12 mat α 2360 * ° * < α σ 1113 mat transpose diag γ * stretch x: X X α σ 2 var2str strrep 12 mat α 2.5 360 * ° * < 1 α σ 113 mat transpose diag γ * stretch y: X X α σ 2 var2str strrep 12 mat α 3360 * ° * < 11 α σ 13 mat transpose diag γ * stretch z: X X α σ 2 var2str strrep 12 mat cases :

Italics

s it fo Word s 0 it 11 i + i 014 fo 0 txtWord 11 line :

Rotate and make complex

T γ txt T γ * 1 col i T γ * 2 col * + eval txtPlot :

Text & hyperboloid of one sheet

α 0360 3.5 * (5 range ° * :

τ 1 α length range :

T 0.2 SMath 0.3 ~Φ00 Word ReIm * : T T 1 col 3.5 - 2 - T 2 col augment : z φ h 0.25 z 2^+ sqrt φ cos * 1 + 0.25 z 2^+ sqrt φ sin * 2 + z 31 mat : H h 1.5 - 2.5 0 1.5 π * 1218 CreateMesh : Anim γ msg 12 mat α t el Anim : 3 γ axis H γ * 13 - msg 13 mat T γ txt 51 sys 21 line : 51 line

Anim

Alvaro

4 appVersion 1.0.8348.30405