lenfant_dc.gcl

% Surveyor’s Layout Instructions for L’Enfant’s First Grand Plan of Washington, D.C.
% Copyright © 2021, by Christopher A. Mosher, Shelton, Connecticut, USA.

% Pierre Charles L’Enfant, dotted line map of Washington, D.C., 1791, before Aug. 19th, https://lccn.loc.gov/88694203 .

dim 223 150

% These constants are only used for proportionally adjusting the drawing to fit the display area. They
% do not otherwise affect the geometry.
number scal 0.012
number offX 152
number offY 40



% L'Enfant first set the positions of the White House
% and the Capitol building, with "vistas" down the
% Potomac River.

% Set Capitol upon Jenkin's Hill.
% Use this is the origin of our two-dimensional
% Cartesian coordinate system.
expression C_x {0*scal+offX}
expression C_y {0*scal+offY}

% Set White House on Beall's Levels.
% Position specified here as relative to the Capitol, in feet.
expression W_x  {-7827*scal+offX}
expression W_y  {2832*scal+offY}

% DC's southern boundary point.
% Alexandria, Virginia was at the extreme southern point
% of the new area of land set aside to be DC.
% L'Enfant and George Washington both had hopes
% of Alexandria being the main port city of the new nation.
expression A_x {-8984*scal+offX}
expression A_y {-36228*scal+offY}

% L'Enfant allowed for a reasonable width (about 160 feet)
% for buildings, and aligned streets to the entrances on either
% side of the White House and the Capitol building. This allowed
% for "vistas" from the entrances, down the streets. Whereas
% aligning streets to the centerpoints of the buildings would
% not achieve this goal.
expression b {160*scal}
expression bneg {-b}

background 255 247 228
fontsize 4


% For streets that are drawn to arbitrary lengths
% off into the margins of the map, we use a distance
% here, for our plotting, that extends far enough past
% other streets. 10 miles is more than enough.
% "f" for "far"
expression f {52800*scal}
% used as directional vectors:
expression negf {-f}
point t 0 0
point tn 0 f
point ts 0 negf
point te f 0
point tw negf 0



% magenta
color 210 57 130

% Capitol building (centerpoint)
point C C_x C_y
cmark_t C
% western entrance
expression Cw_x { C_x - b/2 }
point Cw Cw_x C_y
mark_lb Cw
% eastern entrance
expression Ce_x { C_x + b/2 }
point Ce Ce_x C_y
mark_rb Ce

% White House (centerpoint)
point W W_x W_y
cmark_r W

% northern entrance
expression Wn_y { W_y + b/2 }
point Wn W_x Wn_y
mark_lt Wn
% southern entrance
expression Ws_y { W_y - b/2 }
point Ws W_x Ws_y
mark_lb Ws





% Pennsylvania Av (between White House and Capitol)
line AvPA2 Cw Ws
drawsegment Ws Cw




% green
color 141 153 0

% Jefferson Pier, due S of W, due W of C
point J W_x C_y
mark_lb J

% Capitol Av, N/S and E/W through C
translate Cns t tn C
line CapitolNS C Cns
drawline CapitolNS
translate Cew t te C
line CapitolEW C Cew
drawline CapitolEW

% F St
translate Wew t te Ws
line StF Ws Wew
drawline StF

% 16th St
translate St16f t tn Wn
line St16 Wn St16f
drawsegment Wn St16f

% calculate first angle of avenues (~70 degrees)
angle_o Ap70 Ws Cw J
angle_o An70 J Cw Ws

% Indiana Av
%symmetrical AvINp CapitolEW Ws
%line AvIN J AvINp
rotate RotAvIN J Ap70 Cw
line AvIN1 J RotAvIN
% We can't draw Indiana Av yet, because it's shown to end
% at 4 1/2 St, but we haven't calcluated 4 1/2 St yet.


% New York Av (SW of White House)
symmetrical AvNY1p St16 Cw
line AvNY1 Ws AvNY1p
drawsegment Ws AvNY1p

% C St
intersection AvIN1_x_AvPA2 AvIN1 AvPA2
translate AvIN1_x_AvPA2e t te AvIN1_x_AvPA2
line StC AvIN1_x_AvPA2 AvIN1_x_AvPA2e
drawline StC

% 8th St
mediatrice St8 J Cw
drawline St8

% Maryland Av (SW of Capitol)
translate AvMD1a t tw Cw
rotate RotAvMD1 Cw Ap70 AvMD1a
line AvMD1 Cw RotAvMD1
drawsegment Cw RotAvMD1

% Virginia Av
translate AvVAa t te J
rotate RotAvVA J An70 AvVAa
line AvVA J RotAvVA
drawsegment J RotAvVA











% yellow
color 188 136 1
% Alexandria, Virginia
point A A_x A_y

% Delaware Av SW
line AvDE1 Cw A
drawsegment Cw A

% New Jersey Av SE
symmetrical AvNJ2f CapitolNS A
line AvNJ2 Ce AvNJ2f
drawsegment Ce AvNJ2f






%blue
color 0 141 210

% Calculate the "diamond" shaped avenues just east of
% the Capitol. Its N/S distance is equal to twice the N/S distance
% on 8th St from Capitol Av to Pennsylvania Av; and its E/W
% distance is twice its N/S distance.
% On the original digitized map, these measurements are
% accurate to within 1 one pixel of each other.
intersection CapitiolEW_x_St8 CapitolEW St8
distance h CapitiolEW_x_St8 AvIN1_x_AvPA2
expression h {Ce_x + 4*h}
point L h C_y
mark_rb L

% 5th St E
mediatrice St5E Ce L
drawline St5E

% 12th St E
parallel St12E L St5E
drawline St12E

intersection T St5E StC
mark_rt T

% Massachusetts Av
% Heading NW from L, Massachusetts Av appears mostly straight,
% but is actually crooked by about 2°. Placing a straightedge on the
% original dotted-line map reveals this. Perhaps L'Enfant was following
% the natural elevations of the land, or was adjusting the course to run
% through previously placed "parks" for example at V, Mount Vernon Square.
line AvMA2 T L
intersection CapitolNS_x_AvMA CapitolNS AvMA2
drawsegment L CapitolNS_x_AvMA
rotate AvMAp CapitolNS_x_AvMA 1.8 T
line AvMA AvMAp CapitolNS_x_AvMA
towards AvMAf AvMAp CapitolNS_x_AvMA f
drawsegment CapitolNS_x_AvMA AvMAf

% N St
intersection AvMA_x_St16 AvMA St16
translate StNf t te AvMA_x_St16
line StN AvMA_x_St16 StNf
drawline StN

% K St
intersection V AvMA St8
translate StKf t te V
line StK V StKf
drawline StK

% This point, upon which L'Enfant placed a "park", seems highly significant.
% This became Mount Vernon Square.
mark_rt V









% yellow
color 188 136 1

% New Jersey Av NW
symmetrical AvNJ1f CapitolEW A
line AvNJ1 Cw AvNJ1f
intersection AvNJ1f AvNJ1 StK
drawsegment Cw AvNJ1f

% Delaware Av NE
symmetrical AvDE2f CapitolNS AvNJ1f
line AvDE2 Ce AvDE2f
drawsegment Ce AvDE2f


% 1st St W
intersection AvMa_x_AvNJ1 AvMA AvNJ1
translate St1Wf t tn AvMa_x_AvNJ1
line St1W AvMa_x_AvNJ1 St1Wf
intersection St1Wf St1W AvDE1
drawsegment AvMa_x_AvNJ1 St1Wf

% 1st St E
intersection AvMa_x_AvDE2 AvMA AvDE2
translate St1Ef t tn AvMa_x_AvDE2
line St1E AvMa_x_AvDE2 St1Ef
intersection St1Ef St1E AvNJ2
drawsegment AvMa_x_AvDE2 St1Ef

% E St
translate StEf t te AvMa_x_AvDE2
line StE AvMa_x_AvDE2 StEf
drawline StE

% G St (E of Massachusetts Av)
intersection AvMA_x_AvNJ1 AvMA AvNJ1
translate StG2f t te AvMA_x_AvNJ1
line StG2 AvMA_x_AvNJ1 StG2f
drawsegment AvMA_x_AvNJ1 StG2f





% 4 1/2 St
% This computation is still open for debate, but it appears
% to be halfway between 8th St W and 1st St W
intersection CapitolEW_x_St8 CapitolEW St8
intersection CapitolEW_x_St1W CapitolEW St1W
mediatrice St4_1_2 CapitolEW_x_St8 CapitolEW_x_St1W
drawline St4_1_2





% green
color 141 153 0
% G St
% Distance from White House front entrance to
% G St is approximately the same distance allowed for
% the buildings' depth
translate StGp Ws Wn Wn
translate StGf t tw StGp
line StG StGp StGf
intersection StGp StG AvNJ1
drawsegment StGp StGf


% continue with Indiana Av
intersection AvIN1_x_St4_1_2 AvIN1 St4_1_2
drawsegment J AvIN1_x_St4_1_2
symmetrical AvIN2f St4_1_2 J
line AvIN2 AvIN1_x_St4_1_2 AvIN2f
intersection AvIN2_x_AvNJ1 AvIN2 AvNJ1
drawsegment AvIN1_x_St4_1_2 AvIN2_x_AvNJ1







% yellow
color 188 136 1

% D St
translate StDf t te AvIN1_x_St4_1_2
line StD AvIN1_x_St4_1_2 StDf
drawline StD





%blue
color 0 141 210

% New York Av (NE of White House)
line AvNY2 Wn V
towards AvNY2f Wn V f
drawsegment Wn AvNY2f

% Pennsylvania Av (W of White House)
symmetrical AvPA1f St16 AvNY2f
line AvPA1 Wn AvPA1f
drawsegment Wn AvPA1f

% 23rd St
intersection AvPA1_x_StK AvPA1 StK
translate St23f t tn AvPA1_x_StK
line St23 AvPA1_x_StK St23f
drawline St23

% Maryland Av (NE of Capitol)
line AvMD2 Ce T
towards AvMDf Ce T f
drawsegment Ce AvMDf

% Pennsylvania Av (E of Capitol)
sim S CapitolEW T
mark_rb S
line AvPA3 Ce S
towards AvPA3f Ce S f
drawsegment Ce AvPA3f

% North Carolina Av
line AvNC S L
drawsegment S L







% orange
color 208 76 21

% Vermont Av
% This is within one degree of being perpendicular with Massachusetts Ave
% at their point of intersection. Vermont is even closer to being
% perpendicular to other segemnts of Massachuasetts Av (e.g., east of 4 1/2 St).
perp AvVT Wn AvMA
intersection AvMA_x_AvVT AvMA AvVT
towards AvVTf Wn AvMA_x_AvVT f
drawsegment Wn AvVTf

% M St
translate StMf t te AvMA_x_AvVT
line StM AvMA_x_AvVT StMf
drawline StM

% Connecticut Av
symmetrical AvCTf St16 AvMA_x_AvVT
line AvCT Wn AvCTf
intersection AvMA_x_AvCT AvMA AvCT
drawsegment Wn AvMA_x_AvCT

% P St
translate StPf t te AvMA_x_AvCT
line StP AvMA_x_AvCT StPf
intersection AvVT_x_StP AvVT StP
drawsegment AvMA_x_AvCT AvVT_x_StP

% New Hampshire Av
line AvNH AvPA1_x_StK AvMA_x_AvCT
towards AvNHf AvPA1_x_StK AvMA_x_AvCT f
drawsegment AvPA1_x_StK AvNHf

% Rhode Island Av
intersection AvCT_x_StM AvCT StM
line AvRI AvMA_x_St16 AvCT_x_StM
towards AvRIf AvCT_x_StM AvMA_x_St16 f
drawsegment AvCT_x_StM AvRIf

% 13th St
translate St13f t tn AvVT_x_StP
line St13 AvVT_x_StP St13f
drawline St13

% 14th St
translate St14f t tn AvMA_x_AvVT
line St14 AvMA_x_AvVT St14f
drawline St14

% 19th St
translate St19f t tn AvMA_x_AvCT
line St19 AvMA_x_AvCT St19f
drawline St19

% 18th St (alternate)
translate St18Af t tn AvCT_x_StM
line St18A AvCT_x_StM St18Af
drawsegment AvCT_x_StM St18Af

% 15th St (lower part)
intersection AvCT_x_StK AvCT StK
translate St15Lf t ts AvCT_x_StK
line St15L AvCT_x_StK St15Lf
drawsegment AvCT_x_StK St15Lf

% 17th St (lower part)
symmetrical AvVT_x_StK St16 AvCT_x_StK
symmetrical St17Lf St16 St15Lf
line St17L AvVT_x_StK St17Lf
drawsegment AvVT_x_StK St17Lf

% H St (in front of White House, from 15th St to 19th St)
intersection AvNY2_x_St13 AvNY2 St13
intersection AvPA1_x_St19 AvPA1 St19
line StH2 AvNY2_x_St13 AvPA1_x_St19
drawsegment AvNY2_x_St13 AvPA1_x_St19








% cyan
color 32 162 153

% This next set of streets seems to be determined by first
% setting a standard width for the areas dedicated to "parks"
expression d {200*scal}
expression dneg {-d}
point bn 0 d
point bs 0 dneg
point be d 0
point bw dneg 0

expression d2 {160*scal}
expression d2neg {-d2}
point b2n 0 d2
point b2s 0 d2neg
point b2e d2 0
point b2w d2neg 0

% 17th St (upper part, N of CT Av)
translate St17U_x_StK t be AvCT_x_StK
translate St17Uf t tn St17U_x_StK
line St17U St17U_x_StK St17Uf
intersection AvCT_x_St17U AvCT St17U
drawsegment AvCT_x_St17U St17Uf
fillrectangle AvCT_x_St17U AvCT_x_StK

% 15th St (upper part, N of VT Av)
translate St15U_x_StK t bw AvVT_x_StK
translate St15Uf t tn St15U_x_StK
line St15U St15U_x_StK St15Uf
intersection AvVT_x_St15U AvVT St15U
drawsegment AvVT_x_St15U St15Uf
fillrectangle AvVT_x_St15U AvVT_x_StK

% I St (between NY Av and PA Av)
line StIU AvCT_x_St17U AvVT_x_St15U
intersection StIU_x_AvPA1 StIU AvPA1
intersection StIU_x_AvNY2 StIU AvNY2
drawsegment StIU_x_AvPA1 StIU_x_AvNY2

% 21st St
translate St21f t tn StIU_x_AvPA1
line St21 StIU_x_AvPA1 St21f
drawline St21

% H St (between NY Av and MA Av)
intersection St13_x_StH2 St13 StH2
translate St13_x_StH3 t b2s St13_x_StH2
translate StH3f t te St13_x_StH3
line StH3 St13_x_StH3 StH3f
intersection StH3_x_AvNY2 StH3 AvNY2
intersection StH3_x_AvMA StH3 AvMA
drawsegment StH3_x_AvNY2 StH3_x_AvMA
fillrectangle StH3_x_AvNY2 St13_x_StH2

% 3rd St
translate St3f t tn StH3_x_AvMA
line St3 StH3_x_AvMA St3f
drawline St3

% I St (E of NY Av)
translate StILp t b2s StIU_x_AvNY2
translate StILf t te StIU_x_AvNY2
line StIL StILp StILf
intersection StIL_x_AvNY2 StIL AvNY2
intersection StIL_x_AvMA StIL AvMA
drawsegment StIL_x_AvNY2 StIL_x_AvMA
fillrectangle StIL_x_AvNY2 StIU_x_AvNY2

% 5th St
translate St5f t tn StIL_x_AvMA
line St5 StIL_x_AvMA St5f
drawline St5

% 4th St
symmetrical St4p St4_1_2 StIL_x_AvMA
translate St4f t tn St4p
line St4 St4p St4f
drawline St4

% 11th St
towards St11p StIL_x_AvNY2 StIU_x_AvNY2 0.5
translate St11f t tn St11p
line St11 St11p St11f
drawline St11

% L St (between 4 1/2 St and 11 St)
intersection St5_x_AvNY2 St5 AvNY2
translate St5f t te St5_x_AvNY2
line StLU St5_x_AvNY2 St5f
intersection StLU_x_St4 StLU St4
intersection StLU_x_St11 StLU St11
drawsegment StLU_x_St4 StLU_x_St11

% use the park width N & S of K St to calculate
% positions of 7th St and 9th St
expression halfb {d/2}
expression neghalfb {-d/2}
point halfbn 0 halfb
point halfbs 0 neghalfb
translate V2p t halfbn V
translate V2f t te V2p
line V2 V2p V2f

% 9th St
intersection St9_x_AvMA V2 AvMA
translate St9f t tn St9_x_AvMA
line St9 St9_x_AvMA St9f
drawline St9

% 7th St
intersection St7_x_AvNY2 V2 AvNY2
translate St7f t tn St7_x_AvNY2
line St7 St7_x_AvNY2 St7f
drawline St7

% 10th St (half way between 9th and 11th)
intersection St9_x_StM St9 StM
intersection St11_x_StM St11 StM
mediatrice St10 St9_x_StM  St11_x_StM
drawline St10

% 2nd St (same distance from 3rd St as 10th St is from 11th st)
intersection St10_x_StM St10 StM
intersection St3_x_StM St3 StM
translate St2p St11_x_StM St10_x_StM St3_x_StM
translate St2f t tn St2p
line St2 St2p St2f
drawline St2

% 6th St (Seems almost arbitrarily placed, since it doesn't
% intersect with any other intersections. But it is nearly 3/7ths
% the distance from 5th St to 7th St. That is, the distance from
% 5th to 6th is 3/4 the distance from 6th to 7th.)
expression St6d {3/7}
intersection St5_x_StM St5 StM
intersection St7_x_StM St7 StM
towards St6p St5_x_StM St7_x_StM St6d
translate St6f t tn St6p
line St6 St6p St6f
drawline St6

% 24th St (Seems very arbitrarily placed. The distance from
% 24th St to 23rd St is 3/8 the distance from 21st St to 23rd St.
expression St24d {1+3/8}
intersection St21_x_StM St21 StM
intersection St23_x_StM St23 StM
towards St24p St21_x_StM St23_x_StM St24d
translate St24f t tn St24p
line St24 St24p St24f
drawline St24


% L St (W of Massashusetts Av, and E of 4 1/2 st)
intersection AvNY2_x_St4_1_2 AvNY2 St4_1_2
translate StL1p t bs AvNY2_x_St4_1_2
translate StL1fe t te StL1p
translate StL1fw t tw StL1p
line StL1 StL1p StL1fe
intersection StL1_x_AvMA StL1 AvMA
intersection StL1_x_AvNY2 StL1 AvNY2
drawsegment StL1_x_AvMA StL1fw
drawsegment StL1_x_AvNY2 StL1fe

% 18th St (midway between M St and N St on Connecticut Av)
intersection AvCT_x_StN AvCT StN
towards St18p AvCT_x_StM AvCT_x_StN 0.5
translate St18f t tn St18p
line St18 St18p St18f
drawline St18

% H St (W of Pennsylvania Av)
intersection AvPA1_x_St18 AvPA1 St18
translate StH1f t tw AvPA1_x_St18
line StH1 AvPA1_x_St18 StH1f
drawsegment AvPA1_x_St18 StH1f





% fill in the remaining "parks"
fillrectangle AvCT_x_StN AvCT_x_StM
fillrectangle AvPA1_x_St19 AvPA1_x_St18
intersection St7_x_AvMA St7 AvMA
fillrectangle St7_x_AvMA St9_x_AvMA
intersection St7_x_StF St7 StF
intersection St9_x_StG St9 StG
fillrectangle St7_x_StF St9_x_StG
intersection St7_x_Capitol St7 CapitolEW
intersection St9_x_AvPA2 St9 AvPA2
fillrectangle St7_x_Capitol St9_x_AvPA2
fillrectangle StL1_x_AvNY2 AvNY2_x_St4_1_2
intersection StH3_x_St5 StH3 St5
intersection StD_x_St4 StD St4
fillrectangle StH3_x_St5 StD_x_St4
intersection AvIN2_x_St1W AvIN2 St1W
fillrectangle AvIN2_x_AvNJ1 AvIN2_x_St1W

% Define Thomas Circle Park. Note that this is only
% circular, curved, or arc shaped feature in the entire plan.
translate CirTp t b2n AvMA_x_AvVT
circle CirT AvMA_x_AvVT CirTp
fillcircle CirT



% Street Labels


color 99 123 131



% Label E/W (letter) streets
point tlab 2 0
translate Lewp t tlab L
translate Lewf t tn Lewp
line Lew Lewp Lewf

intersection lab Lew CapitolEW
point lcap -15 0
translate lab t lcap lab
printat lab {Capitol Av}
intersection lab Lew StC
printat lab {C}
intersection lab Lew StD
printat lab {D}
intersection lab Lew StE
printat lab {E}
intersection lab Lew StF
printat lab {F}
intersection lab Lew StG2
printat lab {G}
intersection lab Lew StH3
printat lab {H}
intersection lab Lew StIL
printat lab {I}
intersection lab Lew StK
printat lab {K}
intersection lab Lew StL1
printat lab {L}
intersection lab Lew StM
printat lab {M}
intersection lab Lew StN
printat lab {N}
intersection lab Lew StP
printat lab {P}



% Label N/S (number) streets
point tlab 0 10
translate Lnsp t tlab AvMA_x_AvCT
translate Lnsf t te Lnsp
line Lns Lnsp Lnsf

intersection lab Lns St12E
printat lab {12E}
intersection lab Lns St5E
printat lab {5E}
intersection lab Lns St1E
printat lab {1E}
intersection lab Lns CapitolNS
printat lab {Capitol Av}
intersection lab Lns St1W
printat lab {1}
intersection lab Lns St2
printat lab {2}
intersection lab Lns St3
printat lab {3}
intersection lab Lns St4
printat lab {4}
intersection lab Lns St4_1_2
printat lab {4h}
intersection lab Lns St5
printat lab {5}
intersection lab Lns St6
printat lab {6}
intersection lab Lns St7
printat lab {7}
intersection lab Lns St8
printat lab {8}
intersection lab Lns St9
printat lab {9}
intersection lab Lns St10
printat lab {10}
intersection lab Lns St11
printat lab {11}
intersection lab Lns St13
printat lab {13}
intersection lab Lns St14
printat lab {14}
intersection lab Lns St15U
printat lab {15}
intersection lab Lns St16
printat lab {16}
intersection lab Lns St17U
printat lab {17}
intersection lab Lns St18
printat lab {18}
intersection lab Lns St19
printat lab {19}
intersection lab Lns St21
printat lab {21}
intersection lab Lns St23
printat lab {23}
intersection lab Lns St24
printat lab {24}