1 
NOTE: GLK's approximate ranking of 5 most important tagged with 
NOTE: GLK's approximate ranking of 8 most important tagged with 
2 
[GLK:1], [GLK:2], ... 
[GLK:1], [GLK:2], ... 
3 


4 
============================== 
======================== 
5 
other SHORT TERM ============= (including needed for LIC) 
SHORT TERM ============= (*needed* for streamlines & tractography) 
6 
============================== 
======================== 
7 


8 
Add a clamp function, which takes three arguments; either three scalars: 
[GLK:2] Add sequence types (needed for evals & evecs) 

clamp(x, minval, maxval) = max(minval, min(maxval, x)) 


or three vectors of the same size: 


clamp([x,y], minvec, maxvec) = [max(minvec[0], min(maxvec[0], x)), 


max(minvec[1], min(maxvec[1], y))] 


This would be useful in many current Diderot programs. 


One question: clamp(x, minval, maxval) is the argument order 


used in OpenCL and other places, but clamp(minval, maxval, x) 


would be more consistent with lerp(minout, maxout, x). 





Level of differentiability in field type should be statement about how 


much differentiation the program *needs*, rather than what the kernel 


*provides*. The needed differentiability can be less than or equal to 


the provided differentiability. 





[GLK:1] Add sequence types (needed for evals & evecs) 

9 
syntax 
syntax 
10 
types: ty '{' INT '}' 
types: ty '{' INT '}' 
11 
value construction: '{' e1 ',' … ',' en '}' 
value construction: '{' e1 ',' … ',' en '}' 
12 
indexing: e '{' e '}' 
indexing: e '{' e '}' 
13 


14 
IL support for higherorder tensor values (matrices, etc). 
[GLK:3] evals & evecs for symmetric tensor[2,2] and 
15 
tensor construction [DONE] 
tensor[3,3] (requires sequences) 

tensor indexing [DONE] 


tensor slicing 


verify that hessians work correctly [DONE] 

16 


17 
Use ∇⊗ etc. syntax 
ability to emit/track/record variables into dynamically resized 
18 
syntax [DONE] 
runtime output buffer 

typechecking 


IL and codegen 

19 


20 
test/uninit.diderot: 
[GLK:4] tensor fields from tensor images: Initially need at least 
21 
documents need for better compiler error messages when output variables 
convolution on tensor[2,2] and tensor[3,3] (the same componentwise 
22 
are not initialized; the current messages are very cryptic 
convolution as for vectors). 
23 


24 
determinant ("det") for tensor[3,3] 
======================== 
25 

SHORTISH TERM ========= (to make using Diderot less annoying to 
26 

======================== program in, and slow to execute) 
27 


28 
expand trace in mid to low translation 
Allow ".ddro" file extensions in addition to ".diderot" 
29 


30 
valuenumbering optimization 
Be able to output values of type tensor[2,2] and tensor[3,3]; 
31 

(currently only scalars & vectors). Want to add some regression tests 
32 

based on this and currently can't 
33 


34 
Add type aliases for color types 
[GLK:1] Proper handling of stabilize method 

rgb = real{3} 


rgba = real{4} 

35 


36 
============================== 
Convolution on general tensor images (order > 2) 

MEDIUM TERM ================== (including needed for streamlines & tractography) 


============================== 

37 


38 
[GLK:1] evals & evecs for symmetric tensor[3,3] (requires sequences) 
allow "*" to represent "modulate": percomponent multiplication of 
39 

vectors, and vectors only (not tensors of order 2 or higher). Once 
40 

sequences are implemented this should be removed: the operation is not 
41 

invariant WRT basis so it is not a legit vector computation. 
42 


43 
[GLK:2] Save Diderot output to nrrd, instead of "mip.txt" 
implicit type promotion of integers to reals where reals are 
44 

required (e.g. not exponentiation "^") 
45 


46 

[Nick working on this] Save Diderot output to nrrd, instead of "mip.txt" 
47 
For grid of strands, save to similarlyshaped array 
For grid of strands, save to similarlyshaped array 
48 
For list of strands, save to long 1D (or 2D for nonscalar output) list 
For list of strands, save to long 1D (or 2D for nonscalar output) list 
49 
For ragged things (like tractography output), will need to save both 
For ragged things (like tractography output), will need to save both 
50 
complete list of values, as well as list of start indices and lengths 
complete list of values, as well as list of start indices and lengths 
51 
to index into complete list 
to index into complete list 
52 


53 
[GLK:3] Use of Teem's "hest" commandline parser for getting 
[GLK:6] ability to declare a field so that probe positions are 

any input variables that are not defined in the source file 





[GLK:4] ability to declare a field so that probe positions are 

54 
*always* "inside"; with various ways of mapping the known image values 
*always* "inside"; with various ways of mapping the known image values 
55 
to nonexistant index locations. One possible syntax emphasizes that 
to nonexistant index locations. One possible syntax emphasizes that 
56 
there is a index mapping function that logically precedes convolution: 
there is a index mapping function that logically precedes convolution: 
59 
F = bspln3 ⊛ (img ◦ mirror) 
F = bspln3 ⊛ (img ◦ mirror) 
60 
where "◦" or "∘" is used to indicate function composition 
where "◦" or "∘" is used to indicate function composition 
61 


62 
extend norm (exp) to all tensor types [DONE for vectors and matrices] 
Level of differentiability in field type should be statement about how 
63 

much differentiation the program *needs*, rather than what the kernel 
64 
ability to emit/track/record variables into dynamically resized 
*provides*. The needed differentiability can be less than or equal to 
65 
runtime buffer 
the provided differentiability. 
66 


67 
Want: allow X *= Y, X /= Y, X += Y, X = Y to mean what they do in C, 
Use ∇⊗ etc. syntax 
68 
provided that X*Y, X/Y, X+Y, XY are already supported. 
syntax [DONE] 
69 
Nearly every Diderot program would be simplified by this. 
typechecking 
70 

IL and codegen 
71 


72 
Want: nontrivial field expressions & functions: 
Add type aliases for color types 
73 
image(2)[2] Vimg = load(...); 
rgb = real{3} 
74 
field#0(2)[] Vlen = Vimg ⊛ bspln3; 
rgba = real{4} 

to get a scalar field of vector length, or 


field#2(2)[] F = Fimg ⊛ bspln3; 


field#0(2)[] Gmag = ∇F; 


to get a scalar field of gradient magnitude, or 


field#2(2)[] F = Fimg ⊛ bspln3; 


field#0(2)[] Gmsq = ∇F•∇F; 


to get a scalar field of squared gradient magnitude, which is simpler 


to differentiate. However, there is value in having these, even if 


the differentiation of them is not supported (hence the indication 


of "field#0" for these above) 





Want: ability to apply "normalize" to a field itself, e.g. 


field#0(2)[2] V = normalize(Vimg ⊛ ctmr); 


so that V(x) = normalize((Vimg ⊛ ctmr)(x)). 


Having this would simplify expression of standard LIC method, and 


would also help express other vector field expressions that arise 


in vector field feature exraction. 

75 


76 
tensor fields: convolution on general tensor images 
Revisit how images are created within the language. 
77 

The "load" operator should probably go away, and its strangs 
78 

that strings are there only as a way to refer to nrrd filenames 
79 


80 
============================== 
============================== 
81 
other MEDIUM TERM ============ (needed for particles) 
MEDIUM TERM ================== (*needed* for particles) 
82 
============================== 
============================== 
83 


84 
Put small 1D and 2D fields, when reconstructed specifically by tent 
[Lamont working on this] runtime birth of strands 

and when differentiation is not needed, into faster texture buffers. 


test/illustvr.diderot is good example of program that uses multiple 


such 1D fields basically as lookuptablebased function evaluation 





runtime birth of strands 

85 


86 
"initially" supports lists 
"initially" supports lists 
87 


88 
"initially" supports lists of positions output from 
"initially" supports lists of positions output from different 
89 
different initalization Diderot program 
initalization Diderot program (or output from the same program; 
90 

e.g. using output of iso2d.diderot for one isovalue to seed the input 
91 

to another invocation of the same program) 
92 


93 

[Lamont working on this] Communication between strands: they have to 
94 

be able to learn each other's state (at the previous iteration). 
95 

Early version of this can have the network of neighbors be completely 
96 

static (for running one strand/pixel image computations). Later 
97 

version with strands moving through the domain will require some 
98 

spatial data structure to optimize discovery of neighbors. 
99 


100 

============================ 
101 

MEDIUMISH TERM ============ (to make Diderot more useful/effective) 
102 

============================ 
103 


104 

[GLK:5] Want codegeneration working for tensors of order three. 
105 

Order three matters for edge detection in scalar fields (to get 
106 

second derivatives of gradient magnitude), second derivatives 
107 

of vector fields (for some feature extraction), and first 
108 

derivatives of diffusion tensor fields. 
109 


110 
spatial data structure that permits strands' queries of neighbors 
Python/ctypes interface to runtime 
111 


112 
proper handling of stabilize method 
support for Python interop and GUI 
113 


114 
test/vrkcomp2.diderot: Add support for code like 
Allow integer exponentiation ("^2") to apply to square matrices, 
115 

to represent repeated matrix multiplication 
116 


117 
(F1 if x else F2)@pos 
Put small 1D and 2D fields, when reconstructed specifically by tent 
118 

and when differentiation is not needed, into faster texture buffers. 
119 

test/illustvr.diderot is good example of program that uses multiple 
120 

such 1D fields basically as lookuptablebased function evaluation 
121 


122 
This will require duplication of the continuation of the conditional 
extend norm (exp) to all tensor types [DONE for vectors and matrices] 
123 
(but we should only duplicate over the liverange of the result of the 

124 
conditional. 
determinant ("det") for tensor[3,3] 
125 


126 
add ":" for tensor dot product (contracts out two indices 
add ":" for tensor dot product (contracts out two indices 
127 
instead of one like •), valid for all pairs of tensors with 
instead of one like •), valid for all pairs of tensors with 
128 
at least two indices 
at least two indices 
129 


130 
============================== 
test/uninit.diderot: 
131 
other MEDIUM TERM ============ 
documents need for better compiler error messages when output variables 
132 
============================== 
are not initialized; the current messages are very cryptic 
133 


134 
want: warnings when "D" (reserved for differentiation) is declared as 
want: warnings when "D" (reserved for differentiation) is declared as 
135 
a variable name (get confusing error messages now) 
a variable name (get confusing error messages now) 
136 



support for Python interop and GUI 





Python/ctypes interface to runtime 





============================== 


LONG TERM ==================== 

137 
============================== 
============================== 
138 

LONG TERM ==================== (make Diderot more interesting/attractive from 
139 

============================== a research standpoint) 
140 


141 

IL support for higherorder tensor values (matrices, etc). 
142 

tensor construction [DONE] 
143 

tensor indexing [DONE] 
144 

tensor slicing 
145 


146 
Better handling of variables that determines the scope of a variable 
Better handling of variables that determines the scope of a variable 
147 
based on its actual use, instead of where the user defined it. So, 
based on its actual use, instead of where the user defined it. So, 
149 
scope. Also prune out useless variables, which should include field 
scope. Also prune out useless variables, which should include field 
150 
variables after the translation to midil. 
variables after the translation to midil. 
151 


152 

test/vrkcomp2.diderot: Add support for code like 
153 

(F1 if x else F2)@pos 
154 

This will require duplication of the continuation of the conditional 
155 

(but we should only duplicate over the liverange of the result of the 
156 

conditional. 
157 


158 

[GLK:7] Want: nontrivial field expressions & functions. 
159 

scalar fields from scalar fields F and G: 
160 

field#0(2)[] X = (sin(F) + 1.0)/2; 
161 

field#0(2)[] X = F*G; 
162 

scalar field of vector field magnitude: 
163 

image(2)[2] Vimg = load(...); 
164 

field#0(2)[] Vlen = Vimg ⊛ bspln3; 
165 

field of normalized vectors (for LIC and vector field feature extraction) 
166 

field#2(2)[2] F = ... 
167 

field#0(2)[2] V = normalize(F); 
168 

scalar field of gradient magnitude (for edge detection)) 
169 

field#2(2)[] F = Fimg ⊛ bspln3; 
170 

field#0(2)[] Gmag = ∇F; 
171 

scalar field of squared gradient magnitude (simpler to differentiate): 
172 

field#2(2)[] F = Fimg ⊛ bspln3; 
173 

field#0(2)[] Gmsq = ∇F•∇F; 
174 

There is value in having these, even if the differentiation of them is 
175 

not supported (hence the indication of "field#0" for these above) 
176 


177 

Introduce region types (syntax region(d), where d is the dimension of the 
178 

region. One useful operator would be 
179 

dom : field#k(d)[s] > region(d) 
180 

Then the inside test could be written as 
181 

pos ∈ dom(F) 
182 

We could further extend this approach to allow geometric definitions of 
183 

regions. It might also be useful to do inside tests in world space, 
184 

instead of image space. 
185 


186 
co vs contra index distinction 
co vs contra index distinction 
187 


188 
some indication of tensor symmetry 
Permit field composition: 
189 

field#2(3)[3] warp = bspln3 ⊛ warpData; 
190 

field#2(3)[] F = bspln3 ⊛ img; 
191 

field#2(3)[] Fwarp = F ◦ warp; 
192 

So Fwarp(x) = F(warp(X)). Chain rule can be used for differentation. 
193 

This will be instrumental for expressing nonrigid registration 
194 

methods (but those will require covscontra index distinction) 
195 


196 

Allow the convolution to be specified either as a single 1D kernel 
197 

(as we have it now): 
198 

field#2(3)[] F = bspln3 ⊛ img; 
199 

or, as a tensor product of kernels, one for each axis, e.g. 
200 

field#0(3)[] F = (bspln3 ⊗ bspln3 ⊗ tent) ⊛ img; 
201 

This is especially important for things like timevarying fields 
202 

and the use of scalespace in field visualization: one axis of the 
203 

must be convolved with a different kernel during probing. 
204 

What is very unclear is how, in such cases, we should notate the 
205 

gradient, when we only want to differentiate with respect to some 
206 

subset of the axes. One ambitious idea would be: 
207 

field#0(3)[] Ft = (bspln3 ⊗ bspln3 ⊗ tent) ⊛ img; // 2D timevarying field 
208 

field#0(2)[] F = lambda([x,y], Ft([x,y,42.0])) // restriction to time=42.0 
209 

vec2 grad = ∇F([x,y]); // 2D gradient 
210 


211 

representation of tensor symmetry 
212 
(have to identify the group of index permutations that are symmetries) 
(have to identify the group of index permutations that are symmetries) 
213 


214 
dot works on all tensors 
dot works on all tensors 
215 


216 
outer works on all tensors 
outer works on all tensors 
217 


218 

Help for debugging Diderot programs: need to be able to uniquely 
219 

identify strands, and for particular strands that are known to behave 
220 

badly, do something like printf or other logging of their computations 
221 

and updates. 
222 


223 

Permit writing dimensionally general code: Have some statement of the 
224 

dimension of the world "W" (or have it be learned from one particular 
225 

field of interest), and then able to write "vec" instead of 
226 

"vec2/vec3", and perhaps "tensor[W,W]" instead of 
227 

"tensor[2,2]/tensor[3,3]" 
228 


229 

Traits: all things things that have boilerplate code (especially 
230 

volume rendering) should be expressed in terms of the unique 
231 

computational core. Different kinds of streamline/tractography 
232 

computation will be another example, as well as particle systems. 
233 


234 
Einstein summation notation 
Einstein summation notation 
235 


236 
"tensor comprehension" (like list comprehension) 
"tensor comprehension" (like list comprehension) 
237 


238 

Fields coming from different sources of data: 
239 

* triangular or tetrahedral meshes over 2D or 3D domains (of the 
240 

source produced by finiteelement codes; these will come with their 
241 

own specialized kinds of reconstruction kernels, called "basis 
242 

functions" in this context) 
243 

* Large point clouds, with some radial basis function around each point, 
244 

which will be tuned by parameters of the point (at least one parameter 
245 

giving some notion of radius) 
246 


247 
====================== 
====================== 
248 
BUGS ================= 
BUGS ================= 
249 
====================== 
====================== 
250 



test/read2vecs.diderot: 


// HEY (BUG?) shouldn't it be a type error to load this 2D array of 


// 2vectors into a 2D *scalar* field? Instead, get: 


// uncaught exception Fail [Fail: Error in compiling lic.diderot] 


// raised at driver/main.sml:31.3931.76 


image(2)[] Vimg = load("../data/vorttest.nrrd"); 




251 
test/zslice2.diderot: 
test/zslice2.diderot: 
252 
// HEY (bug) bspln5 leads to problems ... 
// HEY (bug) bspln5 leads to problems ... 
253 
// uncaught exception Size [size] 
// uncaught exception Size [size] 
254 
// raised at ctarget/ctarget.sml:47.1547.19 
// raised at ctarget/ctarget.sml:47.1547.19 
255 
//field#4(3)[] F = img ⊛ bspln5; 
//field#4(3)[] F = img ⊛ bspln5; 
256 

