VISUALIZATION OF LUC CRITERIA: I. VISUAL COMPARISON OF BY-RIGHT, T4A, AND T5A PROCEDURES FOR THE C-2 ZONE II. A PROPER "IMAGE" OF THE LUC AS APPLIED TO THE BIG BOX ORDINANCE. III. MODELING THE LUC: ASSIGNING NUMERICAL VALUES CORRESPONDING TO ELEMENTS OF THE LUC, (last update 9/4/02) ---------------------------------------------------------------------- ---------------------------------------------------------------------- I. VISUAL COMPARISON OF BY-RIGHT, T4A, AND T5A PROCEDURES FOR THE C-2 ZONE From a computer that can handle X-window displays (UNIX, LINUX, IRIX, SOLARIS, etc. operating system, the new apple mac operating system, or msoft with proper addnl software, etc.; BUT NOT STANDARD VANILLA MSOFT OS), login at rupley.com:guest: command line: telnet rupley.com login guest passwd bb--sc netscape (access telnet as URL): telnet://rupley.com which should spawn a command-line window, for login as above You should very shortly after login see displayed an X-window with the Title: "XGobi: luc" and with a standard graph of two coordinates, A1 and A2, with two red, four green, and six yellow points; for viewing convenience each point set is connected by same-color lines. URL: for a GIF image of the "XYPlot" display, point browser at: http://www.urban-issues.com/Images/xgobi-screens/xgobi-luc-init-xy.gif Pull down the "View" menu and select "GrandTour"; the first three variables of the list in the right-hand panel should be displayed along three axes. With time, the orientation of the axes changes randomly, to give different views of the 3-D graph. URL: GIF image, "GrTour" display of three variables: http://www.urban-issues.com/Images/xgobi-screens/xgobi-luc-gr.gif BEST to play at first, until you are comfortable with what is happening, with the default three variables displayed. However, you can display additional axes and variables: click left mouse on one or a small number of the circles that are to the left of the display and that are "empty" = undisplayed (no highlighting of the variable name above). If you wish, all 20 variables can be displayed. BUT, unless you have a very fast data line, response will be slow. URL: GIF image,"GrTour" display of the 11 variables for C2-ByRight: http://www.urban-issues.com/Images/xgobi-screens/xgobi-luc-gr-byrt.gif What is happening? The full explanation is given in section II and III below. Briefly, we have constructed a hyperspace of 20 dimensions, corresponding to the variables A1 to B6, listed on the right-most panel and corresponding to the Performance Criteria of the draft Big Box ordinance: A1 is 3.5.9.7.A.1 (Site Characteristics), etc. Each point in this space corresponds to a particular set of values for the variables (for the standards of the Performance Criteria, A.1 through B.6). The two red points (connected by the red line) correspond to the two sets of values defined for the C-2 Zone by 2.5.4.2.B.5 (two sets because of the "a or b" phrase in the selection of applicable criteria from section A.1). Similarly the four green points correspond to the four sets of values (two "or" phrases) for the T5A Special Exception procedure, and the six yellow points to sets of values for the T4A procedure. Why do the axes and point positions change with time? We cannot view a 20-dimensional object - so we project it onto the 2-D surface of the graph. The length of an axis is proportional to the contribution that the corresponding variable makes to the projected position of a point in the direction of that axis. Clearly, as the lengths and directions of the axes change, the positions of the points must also. The effectively random variation of the axes is to allow the eye to explore all of hyperspace, as a succession of 2-D projected "views". It's not only cute but has been found useful in data mining. Another view (the default when XGobi comes up - image URL given above), of two variables at a time, a bit like what was on the blackboard toward the end of the August 22 BBSC meeting, can be obtained by selecting "XYPlot" from the "View" pull-down menu. Then "FIX Y" with A1 displayed on the Y-axis, and toggle "Cycle" to display all other variables on the X-axis, one by one. Yet another view, of three variables at a time, from selecting "Rotation" from the "View" menu. Fix X and Y axes at A1 and A2 and cycle manually through the other variables for Z-axis display, by clicking left or middle mouse appropriately on variables in the right panel. You can select the axis of rotation. You can by an impulsive motion of the mouse in the center panel display, produce off-axis rotation. This display is closely similar to that for the Grand Tour with three variables selected (image URL given above). ---------------------------------------------------------------------- ---------------------------------------------------------------------- II. A PROPER "GRAPHICAL IMAGE" OF THE LUC AS APPLIED TO THE BIG BOX ORDINANCE. Consider the entire LUC. List every independent element of it. For example, for the 8/29/02 draft, for the Big Box site characteristics there are five elements 3.5.9.7.A.1.a-e, then do this for all other Performance Criteria, then for all procedures, etc. Construct a high-dimensional space, which we will call SpLUC, for which there is a coordinate (axis; "basis vector") for each element of the list. A point (or vector) in SpLUC corresponds to the full description under the LUC of a structure and land use. Specifically, each coordinate corresponding to an element of the LUC that applies to the entity will be non-zero, all other coordinates will be zero. Note that we can assign a numerical value to each coordinate, even for apparently non-numerical elements, e.g., by assigning "1" if true, "0" if false, adding more integers (specifically, powers of 2) if more options than T/F, etc. Consider the space of all elements of the LUC that apply to sites with Big Boxes, which we will call SpLUC-BB. SpLUC-BB is a subspace of SpLUC. We can partition SpLUC-BB into a set of partially overlapping (intersecting) subspaces, SpLUC-BB-Z-AP, each corresponding to a particular Zone and approval procedure, e.g., SpLUC-BB-C2-T3L. Different partitionings of SpLUC are possible, of course, e.g., by Zone, according to the categories and subcategories of permitted uses, of special exception uses, etc. But here we are focused on Big Boxes, not on global description. A table listing elements corresponding to various different Zones/approval procedures for Big Boxes could be pictured by coloring differently in SpLUC-BB the coordinates corresponding to each of the different Zones/approval procedures, e.g., red for the coordinates of SpLUC-BB-C2-T3L, green for SpLUC-BB-C2-ByRight, etc. While one can do this in principle, in one's mind or whatever, to represent the image on paper requires some effort. If one assigns a numerical value to each element of the LUC, i.e, in some way associates a fixed coordinate value with each element, then a table listing elements corresponding to a particular Zone and approval procedure can be represented as a vector in SpLUC (or in the SpLuc-BB... subspace), or equivalently as a point, the endpoint of the vector. One can imagine extensions of this picture. All existing structures in an area under the purview of the LUC map into points in SpLUC. The set of all R-1 structures would lie in a restricted volume of SpLUC; the set of all Big Boxes in another (disjoint) volume. Color one red, the other blue, then twirl or rock the hyperspace (all in one's mind, of course), and admire the nice effect. With some care, one might be able to construct SpLUC in such a way that operators can be developed to transform R-1 into C-2, for example., which would solve many problems that plague developers and politicians. One has a hint of this possibility in the success found for repetitive application of the massive $-operator. But perhaps we get too fanciful (or for those with a different world-view, cynical)..... ---------------------------------------------------------------------- ---------------------------------------------------------------------- III. MODELING THE LUC: ASSIGNING NUMERICAL VALUES CORRESPONDING TO ELEMENTS OF THE LUC, specifically the performance criteria for Big Boxes: 3.5.9.7 For each subsection assign a number and if needed a degeneracy based on the structure of the subsection, e.g.: ---------------------------------------------------------------------- Consider the first subsection, 3.5.9.7.A.1, site characteristics: A.1 site: a vacant, !adjacent historic b redev, !adjacent historic c !adjacent residential, 500' d !adjacent residential, <500' e adjacent residential Assign a unique value to each of the paragraphs A.1.[a-d], such that each combination ("and" = "&") of the paragraphs specified in the zone description is also unique. A simple way to do this is: no selection for this subsection 0 paragraph: a 1 b 2 c 4 d not selected, thus ignore e not selected, thus ignore "and" combinations: a & c 5 b & c 6 The values assigned to the paragraphs (a,b,c) increase in order of (subjective) increasing "difficulty" = restriction. Thus a value for a vector component is related, though not proportional, to its difficulty of implementation and to its restriction of development. Each "or" ("|") relationship between paragraphs creates a two-fold degeneracy, which we handle by evaluating according to the implied parentheses: (a|b)&c = a&c + b&c = 6 + 5 = two points in the subspace SpLUC-BB-C2 or equivalently... = two state vectors in SpLUC-BB = two lines in the matrix (a true matrix) describing the Zone criteria for a Big Box [Note: by assigning successive powers of 2 to the paragraphs, one has a compact computer description: in the block of memory corresponding to a state vector, turn bits on or off according to whether the paragraph is referenced.] ---------------------------------------------------------------------- We now apply this algorithm to the C-2 Zone for the T5A, T4A, and By-Right procedures. In the following Tables of Performance Criteria, values of the vector components are given on the first line for each subsection, with "and" and "or" specified if not obvious from context. The ordering of the paragraphs by increasing difficulty is given in a separate line above each subsection and corresponds to the sequence of values (1,2,4,8,16,...), used in calculating the value(s) for the subsection. Finally, deviating arbitrarily from the algorithm in order to reduce, for pedagogical convenience, the number of coordinates, we sum the values for A.3.a.[1-6] and assign this value 10 to A.3.a, and similarly for A.3.b, A.4.a, A.4.b. Following are the three sets of vectors for the C-2 zone: for the T5A procedure (four vectors for the two 2-fold degenerate subsections), By-Right procedure (2 vectors for the single 2-fold degeneracy), and T4A procedure (6 vectors for one 2- and one 3-fold degeneracy): C-2 ZONE, Type V Administrative Procedure (T5A) Sec. 3.5.9.7. A1 A2 A3a A3b A4a A4b A5 A6 A7 A8 A9 A10 A11 A12 B1 B2 B3 B4 B5 B6 2 8 10 7 10 10 3 3 7 1 7 1 1 0 7 1 1 3 1 7 1 8 10 7 10 10 3 3 7 1 7 1 1 0 7 1 1 3 1 7 2 4 10 7 10 10 3 3 7 1 7 1 1 0 7 1 1 3 1 7 1 4 10 7 10 10 3 3 7 1 7 1 1 0 7 1 1 3 1 7 C-2 ZONE, By-Right Procedure Sec. 3.5.9.7. 6 16 0 0 0 0 0 0 5 1 4 0 0 0 3 1 1 1 1 7 5 16 0 0 0 0 0 0 5 1 4 0 0 0 3 1 1 1 1 7 C-2 ZONE, Type IV Administrative Procedure (T4A ) Sec. 3.5.9.7. 6 8 0 0 0 0 0 0 5 1 4 0 0 0 3 1 1 1 1 7 6 4 0 0 0 0 0 0 5 1 4 0 0 0 3 1 1 1 1 7 6 2 0 0 0 0 0 0 5 1 4 0 0 0 3 1 1 1 1 7 5 8 0 0 0 0 0 0 5 1 4 0 0 0 3 1 1 1 1 7 5 4 0 0 0 0 0 0 5 1 4 0 0 0 3 1 1 1 1 7 5 2 0 0 0 0 0 0 5 1 4 0 0 0 3 1 1 1 1 7 ---------------------------------------------------------------------- ---------------------------------------------------------------------- TABLES OF PERFORMANCE CRITERIA ---------------------------------------------------------------------- SPECIFIED LRE PERFORMANCE CRITERIA, C-2 ZONE, Type V Administrative Procedure (T5A) Sec. 3.5.9.7. with order of difficulty = restriction order: a,b,c (ignore d/e as redundant/not used) A.1. 1,2 a| site: vacant, !adjacent historic + A.1. b site; redev, !adjacent historic + A.1. [c] site; !adjacent residential, 500' A.1. [d] site; !adjacent residential, <500' A.1. [e] site; adjacent residential order: e,d,c,b,a A.2. 4,8 [a] access: arterial, existing A.2. b| access: arterial, 5yr adopted plan + A.2. c access: arterial, dream state + A.2. [d] access: local street, commercial park A.2. [e] access: non-arterial, secondary access order (a.1-4): c,b,a sum: 10 A.3.a.1. 2 b LRE setback: structure 200' A.3.a.2. 2 b LRE setback: outdoor storage 200' A.3.a.3. 2 b LRE setback: trash collection 200' A.3.a.4. 2 b LRE setback: deliv/load, xcpt if enclsd 300' A.3.a.5 1 + LRE setback: deliv park, run & out-hrs 300' A.3.a.6 1 + LRE setback: outdoor sales, 250' order (a.1): b,a sum: 7 A.3.b.1. 1 + non-LRE setback: structure DD A.3.b.2. 1 + non-LRE setback: outdoor storage DD A.3.b.3. 1 + non-LRE setback: trash collection DD A.3.b.4. 2 a non-LRE setback: deliv/load, xcpt if enclsd 200' A.3.b.5 1 + non-LRE setback: deliv park, run & out-hrs 300' A.3.b.6 1 + non-LRE setback: outdoor sales, 250' order (a.1): a,b,c sum: 10 A.4.a.1 7 a LRE buffers: 20' lscpe border, wall 8' A.4.a.1 b LRE buffers: shrubs-etc, trees at 20-30' A.4.a.1 c LRE buffers: no other uses in border area A.4.a.2 1 + LRE buffers: outdoor storage: wall 8' A.4.a.3 1 + LRE buffers: trash collection: wall 8' A.4.a.4 1 + LRE buffers: deliv/load: wall 10' sum: 10 A.4.b 10 + non-LRE buffers: ident. A.4.a order: a,b A.5 3 a hours: no sched. trash collect. 4pm-9am A.5 b hours: no deliv/load adj res. 10pm-7am order: b,a A.6 3 a enforce: tripartite committee A.6 b enforce: posting addr/telno resp. parties order: a,b,c A.7 7 a ped. flows: circulation A.7 b ped. flows: connection adj. res. A.7 c ped. flows: sidewalk areas A.8 1 + site amenities: order: [a,c.1-c.4],b A.9 7 a traffic impacts: analysis report A.9 b traffic impacts: parking generation report A.9 c.1-4 traffic impacts: truck circ setback; PAALs A.10 1 + outdoor lighting: report + mitigation A.11 1 + noise abatement: chap. 11 + no idling 6pm-7am A.12 0 - 10% food restriction order: head,a,b B.1 7 head facades: arch. feat.: reduce scale, mesh env. B.1 a facades: windows etc. in frontage wall B.1 b facades: windows etc. in sides and back walls B.2 1 + detail features: vis. interest, reduce scale B.3 1 + roofs/parapets: eleg. variation, mesh env. order: a,b B.4 3 a materials/colors: low reflec., textured B.4 b materials/colors: mesh env. B.5 1 + entryways: visible order: head,a,b [exception c = 0] B.6 7 head screening mech.: mitigate noise and view B.6 a screening mech.: roof mntd: mesh design B.6 b screening mech.: grnd mntd: mason. screen B.6 c screening mech.: exception: adj. elev. road SPECIFIED LRE PERFORMANCE CRITERIA, C-2 ZONE, Type IV Administrative Procedure (T4A ) Sec. 3.5.9.7. A.1. 5,6 (a| A.1. b)& A.1. c site: >500' from residential A.2. 2,4,8 b| access: arterial, 5yr adopted plan A.2. c| access: arterial, dream state A.2. d access: local street in indus. park, ->arterial A.3.a 0 - LRE setbacks: A.3.b 0 - non-LRE setbacks: A.4.a 0 - LRE buffers: A.4.b 0 - non-LRE buffers: A.5 0 - hours: A.6 0 - enforce: A.7 5 a ped. flows: circulation A.7 c ped. flows: sidewalk areas A.8 1 + site amenities: A.9 4 a traffic impacts: analysis report A.9 b traffic impacts: parking generation report A.9 c.4 traffic impacts: truck circ sep cust. circ. A.10 0 - outdoor lighting: A.11 0 - noise abatement: A.12 0 - 10 % restriction B.1 3 head facades: arch. feat.: reduce scale, mesh env. B.1 a facades: windows etc. in frontage wall B.2 1 + detail features: B.3 1 + roofs/parapets: B.4 1 a materials/colors: low reflec., textured B.5 1 + entryways: B.6 7 + screening mech.: SPECIFIED LRE PERFORMANCE CRITERIA, C-2 ZONE, BY RIGHT: Sec. 3.5.9.7. A.1. 5,6 (a| A.1. b)& A.1. c site: >500' from residential A.2. 16 a access: existing arterial A.3.a 0 - setbacks: A.3.b 0 - setbacks: A.4.a 0 - buffers: A.4.b 0 - buffers: A.5 0 - hours: A.6 0 - enforce: A.7. 5 a& ped. flows: circulation A.7. c ped. flows: sidewalk areas [no A.7.b: connection adj. res.] A.8 1 + site amenities: A.9. 4 a traffic impacts: analysis report A.9. b traffic impacts: parking generation report A.9 c.4 traffic impacts: truck circ sep cust. circ. A.10 0 - outdoor lighting: A.11 0 - noise abatement: A.12 0 - 10 % restriction B.1 3 head facades: arch. feat.: reduce scale, mesh env. B.1 a facades: windows etc. in frontage wall B.2 1 + detail features: B.3 1 + roofs/parapets: B.4. 1 a materials/colors: low reflec., textured [no meshing with environment] B.5 1 + entryways: B.6 7 + screening mech.: