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This to do for the Vis 2012 submission 

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THIS TODO HAS BEEN MOVED TO THE DIDEROT WIKI: 

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http://diderotwiki.cs.uchicago.edu/index.php/Todo 
3rd order tensors: 2x2x2 and 3x3x3 
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PLEASE USE THAT PAGE TO UPDATE PROBLEMS AND PROGRESS 
dynamiclength sequences 

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NOTE: GLK's approximate ranking of 8 most important tagged with 
curl 2D and 3D 

[GLK:1], [GLK:2], ... 

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support iteration over image indices 

SHORT TERM ============= (*needed* for streamlines & tractography) 


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





[GLK:2] Add sequence types (needed for evals & evecs) 


syntax 


types: ty '{' INT '}' 


value construction: '{' e1 ',' … ',' en '}' 


indexing: e '{' e '}' 





[GLK:3] evals & evecs for symmetric tensor[2,2] and 


tensor[3,3] (requires sequences) 





ability to emit/track/record variables into dynamically resized 


runtime output buffer 





[GLK:4] tensor fields from tensor images: Initially need at least 


convolution on tensor[2,2] and tensor[3,3] (the same componentwise 


convolution as for vectors). 





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


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





Allow ".ddro" file extensions in addition to ".diderot" 





Be able to output values of type tensor[2,2] and tensor[3,3]; 


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


based on this and currently can't 





[GLK:1] Proper handling of stabilize method 





Convolution on general tensor images (order > 2) 





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


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


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


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





implicit type promotion of integers to reals where reals are 


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





[Nick working on this] Save Diderot output to nrrd, instead of "mip.txt" 


For grid of strands, save to similarlyshaped array 


For list of strands, save to long 1D (or 2D for nonscalar output) list 


For ragged things (like tractography output), will need to save both 


complete list of values, as well as list of start indices and lengths 


to index into complete list 





[GLK:6] ability to declare a field so that probe positions are 


*always* "inside"; with various ways of mapping the known image values 


to nonexistant index locations. One possible syntax emphasizes that 


there is a index mapping function that logically precedes convolution: 


F = bspln3 ⊛ (img ◦ clamp) 


F = bspln3 ⊛ (img ◦ repeat) 


F = bspln3 ⊛ (img ◦ mirror) 


where "◦" or "∘" is used to indicate function composition 





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. 





Use ∇⊗ etc. syntax 


syntax [DONE] 


typechecking 


IL and codegen 





Add type aliases for color types 


rgb = real{3} 


rgba = real{4} 





Revisit how images are created within the language. 


The "load" operator should probably go away, and its strange 


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





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MEDIUM TERM ================== (*needed* for particles) 


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





[Lamont working on this] runtime birth of strands 





"initially" supports lists 





"initially" supports lists of positions output from different 


initalization Diderot program (or output from the same program; 


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


to another invocation of the same program) 





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


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


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


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


version with strands moving through the domain will require some 


spatial data structure to optimize discovery of neighbors. 





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


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


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





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


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


second derivatives of gradient magnitude), second derivatives 


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


derivatives of diffusion tensor fields. 





Python/ctypes interface to runtime 





support for Python interop and GUI 





Allow integer exponentiation ("^2") to apply to square matrices, 


to represent repeated matrix multiplication 





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 





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





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





add ":" for tensor dot product (contracts out two indices 


instead of one like •), valid for all pairs of tensors with 


at least two indices 





test/uninit.diderot: 


documents need for better compiler error messages when output variables 


are not initialized; the current messages are very cryptic 





want: warnings when "D" (reserved for differentiation) is declared as 


a variable name (get confusing error messages now) 





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


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


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





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


tensor construction [DONE] 


tensor indexing [DONE] 


tensor slicing 





Better handling of variables that determines the scope of a variable 


based on its actual use, instead of where the user defined it. So, 


for example, we should lift strandinvariant variables to global 


scope. Also prune out useless variables, which should include field 


variables after the translation to midil. 





test/vrkcomp2.diderot: Add support for code like 


(F1 if x else F2)@pos 


This will require duplication of the continuation of the conditional 


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


conditional. 





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


scalar fields from scalar fields F and G: 


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


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


scalar field of vector field magnitude: 


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


field#0(2)[] Vlen = Vimg ⊛ bspln3; 


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


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


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


scalar field of gradient magnitude (for edge detection)) 


field#2(2)[] F = Fimg ⊛ bspln3; 


field#0(2)[] Gmag = ∇F; 


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


field#2(2)[] F = Fimg ⊛ bspln3; 


field#0(2)[] Gmsq = ∇F•∇F; 


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


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





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


region. One useful operator would be 


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


Then the inside test could be written as 


pos ∈ dom(F) 


We could further extend this approach to allow geometric definitions of 


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


instead of image space. 





co vs contra index distinction 





Permit field composition: 


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


field#2(3)[] F = bspln3 ⊛ img; 


field#2(3)[] Fwarp = F ◦ warp; 


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


This will be instrumental for expressing nonrigid registration 


methods (but those will require covscontra index distinction) 





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 fields 


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


must be convolved with a different kernel during probing. 


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


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


subset of the axes. One ambitious idea would be: 


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


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


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





representation of tensor symmetry 


(have to identify the group of index permutations that are symmetries) 





dot works on all tensors 





outer works on all tensors 





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


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


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


and updates. 





Permit writing dimensionally general code: Have some statement of the 


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


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


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


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





Traits: all things things that have boilerplate code (especially 


volume rendering) should be expressed in terms of the unique 


computational core. Different kinds of streamline/tractography 


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





Einstein summation notation 





"tensor comprehension" (like list comprehension) 





Fields coming from different sources of data: 


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


source produced by finiteelement codes; these will come with their 


own specialized kinds of reconstruction kernels, called "basis 


functions" in this context) 


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


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


giving some notion of radius) 





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BUGS ================= 


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





test/zslice2.diderot: 


// HEY (bug) bspln5 leads to problems ... 


// uncaught exception Size [size] 


// raised at ctarget/ctarget.sml:47.1547.19 


//field#4(3)[] F = img ⊛ bspln5; 

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