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




Add a clamp function, which takes three arguments; either three scalars: 


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). 

7 


8 
Level of differentiability in field type should be statement about how 
[GLK:3] Add sequence types (needed for evals & evecs) 

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:4] 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 buffer 

typechecking 


IL and codegen 

19 


20 
test/uninit.diderot: 
tensor fields: convolution on general tensor images 

documents need for better compiler error messages when output variables 


are not initialized; the current messages are very cryptic 

21 


22 
determinant ("det") for tensor[3,3] 
======================== 
23 

SHORTISH TERM ========= (to make using Diderot less annoying to 
24 

======================== program in, and slow to execute) 
25 


26 
expand trace in mid to low translation 
valuenumbering optimization [DONE, but needs more testing] 
27 


28 
valuenumbering optimization 
Allow ".ddro" file extensions in addition to ".diderot" 
29 


30 
Add type aliases for color types 
Be able to output values of type tensor[2,2] and tensor[3,3]; 
31 
rgb = real{3} 
(currently only scalars & vectors). Want to add some regression tests 
32 
rgba = real{4} 
based on this and currently can't 
33 


34 
============================== 
[GLK:1] Add a clamp function, which takes three arguments; either 
35 
MEDIUM TERM ================== (including needed for streamlines & tractography) 
three scalars: 
36 
============================== 
clamp(lo, hi, x) = max(lo, min(hi, x)) 
37 

or three vectors of the same size: 
38 

clamp(lo, hi, [x,y]) = [max(lo[0], min(hi[0], x)), 
39 

max(lo[1], min(hi[1], y))] 
40 

This would be useful in many current Diderot programs. 
41 

One question: clamp(x, lo, hi) is the argument order used in OpenCL 
42 

and other places, but clamp(lo, hi, x) is much more consistent with 
43 

lerp(lo, hi, x), hence GLK's preference 
44 


45 

[GLK:2] Proper handling of stabilize method 
46 


47 

allow "*" to represent "modulate": percomponent multiplication of 
48 

vectors, and vectors only (not tensors of order 2 or higher). Once 
49 

sequences are implemented this should be removed: the operation is not 
50 

invariant WRT basis so it is not a legit vector computation. 
51 


52 
[GLK:1] evals & evecs for symmetric tensor[3,3] (requires sequences) 
implicit type promotion of integers to reals where reals are 
53 

required (e.g. not exponentiation "^") 
54 


55 
[GLK:2] Save Diderot output to nrrd, instead of "mip.txt" 
[GLK:5] Save Diderot output to nrrd, instead of "mip.txt" 
56 
For grid of strands, save to similarlyshaped array 
For grid of strands, save to similarlyshaped array 
57 
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 
58 
For ragged things (like tractography output), will need to save both 
For ragged things (like tractography output), will need to save both 
59 
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 
60 
to index into complete list 
to index into complete list 
61 


62 
[GLK:3] Use of Teem's "hest" commandline parser for getting 
[GLK:6] Use of Teem's "hest" commandline parser for getting 
63 
any input variables that are not defined in the source file 
any "input" variables that are not defined in the source file. 
64 


65 
[GLK:4] ability to declare a field so that probe positions are 
[GLK:7] ability to declare a field so that probe positions are 
66 
*always* "inside"; with various ways of mapping the known image values 
*always* "inside"; with various ways of mapping the known image values 
67 
to nonexistant index locations. One possible syntax emphasizes that 
to nonexistant index locations. One possible syntax emphasizes that 
68 
there is a index mapping function that logically precedes convolution: 
there is a index mapping function that logically precedes convolution: 
71 
F = bspln3 ⊛ (img ◦ mirror) 
F = bspln3 ⊛ (img ◦ mirror) 
72 
where "◦" or "∘" is used to indicate function composition 
where "◦" or "∘" is used to indicate function composition 
73 


74 
extend norm (exp) to all tensor types [DONE for vectors and matrices] 
Level of differentiability in field type should be statement about how 
75 

much differentiation the program *needs*, rather than what the kernel 
76 
ability to emit/track/record variables into dynamically resized 
*provides*. The needed differentiability can be less than or equal to 
77 
runtime buffer 
the provided differentiability. 




Want: allow X *= Y, X /= Y, X += Y, X = Y to mean what they do in C, 


provided that X*Y, X/Y, X+Y, XY are already supported. 


Nearly every Diderot program would be simplified by this. 

78 


79 
[GLK:5] Want: nontrivial field expressions & functions: 
Use ∇⊗ etc. syntax 
80 
image(2)[2] Vimg = load(...); 
syntax [DONE] 
81 
field#0(2)[] Vlen = Vimg ⊛ bspln3; 
typechecking 
82 
to get a scalar field of vector length, or 
IL and codegen 

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. 

83 


84 
tensor fields: convolution on general tensor images 
Add type aliases for color types 
85 

rgb = real{3} 
86 

rgba = real{4} 
87 


88 
============================== 
============================== 
89 
other MEDIUM TERM ============ (needed for particles) 
MEDIUM TERM ================== (*needed* for particles) 
90 
============================== 
============================== 
91 



Put small 1D and 2D fields, when reconstructed specifically by tent 


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 




92 
runtime birth of strands 
runtime birth of strands 
93 


94 
"initially" supports lists 
"initially" supports lists 
96 
"initially" supports lists of positions output from 
"initially" supports lists of positions output from 
97 
different initalization Diderot program 
different initalization Diderot program 
98 


99 
spatial data structure that permits strands' queries of neighbors 
Communication between strands: they have to be able to learn each 
100 

other's state (at the previous iteration). Early version of this can 
101 

have the network of neighbors be completely static (for running one 
102 

strand/pixel image computations). Later version with strands moving 
103 

through the domain will require some spatial data structure to 
104 

optimize discovery of neighbors. 
105 


106 

============================ 
107 

MEDIUMISH TERM ============ (to make Diderot more useful/effective) 
108 

============================ 
109 


110 
proper handling of stabilize method 
Python/ctypes interface to runtime 
111 


112 
test/vrkcomp2.diderot: Add support for code like 
support for Python interop and GUI 
113 


114 
(F1 if x else F2)@pos 
Allow integer exponentiation ("^2") to apply to square matrices, 
115 

to represent repeated matrix multiplication 
116 


117 
This will require duplication of the continuation of the conditional 
Alow X *= Y, X /= Y, X += Y, X = Y to mean what they do in C, 
118 
(but we should only duplicate over the liverange of the result of the 
provided that X*Y, X/Y, X+Y, XY are already supported. 
119 
conditional. 
Nearly every Diderot program would be simplified by this. 
120 


121 

Put small 1D and 2D fields, when reconstructed specifically by tent 
122 

and when differentiation is not needed, into faster texture buffers. 
123 

test/illustvr.diderot is good example of program that uses multiple 
124 

such 1D fields basically as lookuptablebased function evaluation 
125 


126 

expand trace in mid to low translation 
127 


128 

extend norm (exp) to all tensor types [DONE for vectors and matrices] 
129 


130 

determinant ("det") for tensor[3,3] 
131 


132 
add ":" for tensor dot product (contracts out two indices 
add ":" for tensor dot product (contracts out two indices 
133 
instead of one like •), valid for all pairs of tensors with 
instead of one like •), valid for all pairs of tensors with 
134 
at least two indices 
at least two indices 
135 


136 
============================== 
test/uninit.diderot: 
137 
other MEDIUM TERM ============ 
documents need for better compiler error messages when output variables 
138 
============================== 
are not initialized; the current messages are very cryptic 
139 


140 
want: warnings when "D" (reserved for differentiation) is declared as 
want: warnings when "D" (reserved for differentiation) is declared as 
141 
a variable name (get confusing error messages now) 
a variable name (get confusing error messages now) 
142 



support for Python interop and GUI 





Python/ctypes interface to runtime 





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


(as we have it now): 


field#2(3)[] F = bspln3 ⊛ img; 


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


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


This is especially important for things like timevarying data, or 


other multidimensional fields where one axis of the domain is very 


different from the rest. What is very unclear is how, in such cases, 


we should notate the gradient, when we only want to differentiate with 


respect to some of the axes. 





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


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

143 
============================== 
============================== 
144 

LONG TERM ==================== (make Diderot more interesting/attractive from 
145 

============================== a research standpoint) 
146 


147 

IL support for higherorder tensor values (matrices, etc). 
148 

tensor construction [DONE] 
149 

tensor indexing [DONE] 
150 

tensor slicing 
151 

verify that hessians work correctly [DONE] 
152 


153 
Better handling of variables that determines the scope of a variable 
Better handling of variables that determines the scope of a variable 
154 
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, 
156 
scope. Also prune out useless variables, which should include field 
scope. Also prune out useless variables, which should include field 
157 
variables after the translation to midil. 
variables after the translation to midil. 
158 


159 

test/vrkcomp2.diderot: Add support for code like 
160 

(F1 if x else F2)@pos 
161 

This will require duplication of the continuation of the conditional 
162 

(but we should only duplicate over the liverange of the result of the 
163 

conditional. 
164 


165 

[GLK:8] Want: nontrivial field expressions & functions. 
166 

scalar fields from scalar fields F and G: 
167 

field#0(2)[] X = (sin(F) + 1.0)/2; 
168 

field#0(2)[] X = F*G; 
169 

scalar field of vector field magnitude: 
170 

image(2)[2] Vimg = load(...); 
171 

field#0(2)[] Vlen = Vimg ⊛ bspln3; 
172 

field of normalized vectors (for LIC and vector field feature extraction) 
173 

field#2(2)[2] F = ... 
174 

field#0(2)[2] V = normalize(F); 
175 

scalar field of gradient magnitude (for edge detection)) 
176 

field#2(2)[] F = Fimg ⊛ bspln3; 
177 

field#0(2)[] Gmag = ∇F; 
178 

scalar field of squared gradient magnitude (simpler to differentiate): 
179 

field#2(2)[] F = Fimg ⊛ bspln3; 
180 

field#0(2)[] Gmsq = ∇F•∇F; 
181 

There is value in having these, even if the differentiation of them is 
182 

not supported (hence the indication of "field#0" for these above) 
183 


184 

Introduce region types (syntax region(d), where d is the dimension of the 
185 

region. One useful operator would be 
186 

dom : field#k(d)[s] > region(d) 
187 

Then the inside test could be written as 
188 

pos ∈ dom(F) 
189 

We could further extend this approach to allow geometric definitions of 
190 

regions. It might also be useful to do inside tests in world space, 
191 

instead of image space. 
192 


193 
co vs contra index distinction 
co vs contra index distinction 
194 


195 
some indication of tensor symmetry 
Permit field composition: 
196 

field#2(3)[3] warp = bspln3 ⊛ warpData; 
197 

field#2(3)[] F = bspln3 ⊛ img; 
198 

field#2(3)[] Fwarp = F ◦ warp; 
199 

So Fwarp(x) = F(warp(X)). Chain rule can be used for differentation. 
200 

This will be instrumental for expressing nonrigid registration 
201 

methods (but those will require covscontra index distinction) 
202 


203 

Allow the convolution to be specified either as a single 1D kernel 
204 

(as we have it now): 
205 

field#2(3)[] F = bspln3 ⊛ img; 
206 

or, as a tensor product of kernels, one for each axis, e.g. 
207 

field#0(3)[] F = (bspln3 ⊗ bspln3 ⊗ tent) ⊛ img; 
208 

This is especially important for things like timevarying fields 
209 

and the use of scalespace in field visualization: one axis of the 
210 

must be convolved with a different kernel during probing. 
211 

What is very unclear is how, in such cases, we should notate the 
212 

gradient, when we only want to differentiate with respect to some 
213 

subset of the axes. One ambitious idea would be: 
214 

field#0(3)[] Ft = (bspln3 ⊗ bspln3 ⊗ tent) ⊛ img; // 2D timevarying field 
215 

field#0(2)[] F = lambda([x,y], Ft([x,y,42.0])) // restriction to time=42.0 
216 

vec2 grad = ∇F([x,y]); // 2D gradient 
217 


218 

Tensors of order 3 (e.g. gradients of diffusion tensor fields, or 
219 

hessians of vector fields) and order 4 (e.g. Hessians of diffusion 
220 

tensor fields). 
221 


222 

representation of tensor symmetry 
223 
(have to identify the group of index permutations that are symmetries) 
(have to identify the group of index permutations that are symmetries) 
224 


225 
dot works on all tensors 
dot works on all tensors 
226 


227 
outer works on all tensors 
outer works on all tensors 
228 


229 

Help for debugging Diderot programs: need to be able to uniquely 
230 

identify strands, and for particular strands that are known to behave 
231 

badly, do something like printf or other logging of their computations 
232 

and updates. 
233 


234 

Permit writing dimensionally general code: Have some statement of the 
235 

dimension of the world "W" (or have it be learned from one particular 
236 

field of interest), and then able to write "vec" instead of 
237 

"vec2/vec3", and perhaps "tensor[W,W]" instead of 
238 

"tensor[2,2]/tensor[3,3]" 
239 


240 

Traits: all things things that have boilerplate code (especially 
241 

volume rendering) should be expressed in terms of the unique 
242 

computational core. Different kinds of streamline/tractography 
243 

computation will be another example, as well as particle systems. 
244 


245 
Einstein summation notation 
Einstein summation notation 
246 


247 
"tensor comprehension" (like list comprehension) 
"tensor comprehension" (like list comprehension) 
248 


249 

Fields coming from different sources of data: 
250 

* triangular or tetrahedral meshes over 2D or 3D domains (of the 
251 

source produced by finiteelement codes; these will come with their 
252 

own specialized kinds of reconstruction kernels, called "basis 
253 

functions" in this context) 
254 

* Large point clouds, with some radial basis function around each point, 
255 

which will be tuned by parameters of the point (at least one parameter 
256 

giving some notion of radius) 
257 


258 
====================== 
====================== 
259 
BUGS ================= 
BUGS ================= 
260 
====================== 
====================== 