R/findJointPaths.R
In aaronolsen/linkR: 3D Lever and Linkage Mechanism Modeling
findJointPaths <- function(body.conn, joint.types, solvable.paths, sole.joints){
# IF A SINGLE JOINT, RETURN 0,1
if(nrow(body.conn) == 1) return(list(
'paths.closed'=NULL,
'paths.open'=list(c(0,1)),
'fixed.joints'=1,
'joint.conn'=NULL
))
## CREATE MATRIX FOR CONNECTED JOINTS
joint.conn <- matrix(NA, nrow=0, ncol=3, dimnames=list(NULL, c('body.idx', 'joint1', 'joint2')))
# GET UNIQUE LINK INDICES
link_idx_unique <- sort(unique(c(body.conn)))
# NUMBER OF JOINTS
num_joints <- nrow(body.conn)
# FILL MATRIX OF CONNECTED JOINTS
for(link_idx in link_idx_unique){
# FIND ALL JOINTS CONNECTED TO LINK
joints_conn <- (1:num_joints)[(rowSums(link_idx == body.conn) == 1)]
# REMOVE NA VALUES
#joints_conn <- joints_conn[!is.na(joints_conn)]
# SKIP IF ONLY SINGLE JOINT CONNECTED
if(length(joints_conn) == 1) next
# GENERATE UNIQUE PAIRS
for(i in 1:(length(joints_conn)-1)){
for(j in (i+1):(length(joints_conn))){
joint.conn <- rbind(joint.conn, c(link_idx, sort(c(joints_conn[i], joints_conn[j]))))
}
}
}
# FIND JOINTS CONNECTED TO FIXED LINK (INCLUDES OPEN CHAIN WITH SINGLE JOINT CONNECTED TO FIXED LINK)
fixed.joints <- which(rowSums(body.conn == 1) > 0)
#fixed.joints <- unique(c(joint.conn[joint.conn[, 1] == 1, 2:3]))
# ADD ROWS FOR JOINTS CONNECTED TO THE FIXED LINK FOR EASIER PATH SEARCHING
joint.conn <- rbind(cbind(rep(1,length(fixed.joints)), rep(0,length(fixed.joints)), fixed.joints), joint.conn)
colnames(joint.conn) <- c('body.idx', 'joint1', 'joint2')
rownames(joint.conn) <- NULL
## FIND ALL JOINT PATHS
# INITIAL PATHS
paths <- list()
for(i in 1:length(fixed.joints)) paths[[i]] <- c(0, fixed.joints[i])
it <- 1
no_change <- FALSE
max_path_len <- 20
# FIND ALL UNIQUE FIXED TO FIXED PATHS
#while(it < 5){
while(no_change == FALSE){
#for(i in 1:length(paths)){cat('P');print(paths[[i]])}
no_change <- TRUE
for(i in 1:length(paths)){
#cat('P');print(paths[[i]])
# SKIP IF LAST JOINT IS NA
if(is.na(paths[[i]][length(paths[[i]])])) next
# SKIP IF LAST JOINT IS CONNECTED TO FIXED
if(paths[[i]][length(paths[[i]])] == 0) next
# SKIP IF PATH EXCEEDS MAXIMUM PATH LENGTH
if(length(paths[[i]]) > max_path_len) next
# GET LAST JOINT IN PATH
last_joint <- paths[[i]][length(paths[[i]])]
# FIND ALL CONNECTED JOINTS
joints_conn_idx <- rowSums(joint.conn[, 2:3] == last_joint) > 0
joints_conn <- unique(c(joint.conn[joints_conn_idx, 2:3]))
# REMOVE JOINTS ALREADY IN PATH EXCEPT ZEROS
joints_conn <- joints_conn[!joints_conn %in% paths[[i]][paths[[i]] > 0]]
# IF LAST JOINT IS JOINT CONNECTED TO FIXED LINK, REMOVE OTHER FIXED LINK JOINTS - AVOIDS LOOPS WITHIN FIXED LINK
if(last_joint %in% fixed.joints) joints_conn <- joints_conn[!joints_conn %in% fixed.joints]
# CHECK IF NO CONNECTED JOINTS
if(length(joints_conn) == 0) next
# REFINE TO LIMIT NUMBER OF LOOPS WITHIN LINK
if(TRUE){
if(length(paths[[i]]) > 1 && paths[[i]][length(paths[[i]])] != 0){
## IF LAST TWO JOINTS ARE WITHIN SAME BODY, REMOVE JOINTS IN THE SAME BODY - AVOIDS LOOPS WITHIN A LINK
# GET LAST TWO JOINTS
last_two <- paths[[i]][(length(paths[[i]])-1):length(paths[[i]])]
# FIND ASSOCIATED BODIES
body1 <- unique(body.conn[last_two[1], ])
body2 <- unique(body.conn[last_two[2], ])
# FIND SAME BODY BETWEEN TWO JOINTS
shared_body <- body1[body1 %in% body2]
# FIND JOINTS
if(length(shared_body) > 0){
# FIND JOINTS CONNECTED TO SHARED BODY
shared_body_joints <- unique(c(joint.conn[joint.conn[, 1] == shared_body, 2:3]))
# REMOVE
joints_conn <- joints_conn[!joints_conn %in% shared_body_joints]
}
# IF ALL CONNECTING JOINTS WERE ELIMINATED BECAUSE THEY WERE IN THE SAME LINK, ADD NA TO FLAG PATH FOR REMOVAL
if(length(joints_conn) == 0){
#paths[[i]] <- c(paths[[i]], NA)
next
}
}
#cat('J2 ');print(joints_conn)
}
# REMOVE ZERO IF PATH IS ONLY TWO JOINTS LONG
if(length(paths[[i]]) == 2) joints_conn <- joints_conn[joints_conn > 0]
# CHECK IF NO CONNECTED JOINTS
if(length(joints_conn) == 0) next
#cat('P');print(paths[[i]])
# SET CHANGE
no_change <- FALSE
# CREATE NEW PATHS IF MORE THAN ONE CONNECTING JOINT
if(length(joints_conn) > 1) for(j in 2:length(joints_conn)) paths[[length(paths)+1]] <- c(paths[[i]], joints_conn[j])
# ADD FIRST CONNECTING JOINT TO CURRENT PATH
paths[[i]] <- c(paths[[i]], joints_conn[1])
#cat('\n')
}
it <- it + 1
}
## BREAK UP CLOSED PATHS INTO FRAGMENTS
# FIND MINIMUM AND MAXIMUM FRAGMENT LENGTH TO SAVE
paths_nchar <- unlist(lapply(gsub('-', '', solvable.paths), 'nchar'))
frag_len_min <- min(paths_nchar)
frag_len_max <- max(paths_nchar)
# ADD REVERSE SOLVABLE PATHS
for(i in 1:length(solvable.paths)) solvable.paths <- c(solvable.paths, paste0(rev(strsplit(solvable.paths[i], '-')[[1]]), collapse='-'))
solvable.paths <- unique(solvable.paths)
# Remove paths with NA - may need to put this later?
#paths <- paths[unlist(lapply(lapply(paths, 'is.na'), 'sum')) == 0]
path_frags <- c()
path_frag_list <- list()
for(path_num in 1:length(paths)){
path <- paths[[path_num]]
# IF OPEN CHAIN SAVE BUT DO NOT BREAK INTO FRAGMENTS
if(path[1] == 0 && tail(path, 1) != 0){
path_frag_list[[length(path_frag_list) + 1]] <- path
next
}
for(frag_len in frag_len_min:min(length(path), frag_len_max)){
for(i in 1:(length(path)-frag_len+1)){
# SAVE PATH AS VECTOR
path_vec <- path[seq(i, i+frag_len-1)]
# REMOVE ZEROS
path_vec <- path_vec[path_vec != 0]
# CHECK IF FRAGMENT ALREADY EXISTS
if(paste(path_vec, collapse='-') %in% path_frags) next
#print(path_vec)
# CHECK IF FRAGMENT TYPE SEQUENCE IS SOLVABLE
if(!paste0(joint.types[path_vec], collapse='-') %in% solvable.paths) next
# MAKE SEQUENCE INTO STRING FOR EASY LOOK-UP
path_string <- paste(path_vec, collapse='-')
# ADD PATH TO VECTOR OF FRAGMENTS
path_frags <- c(path_frags, path_string)
# ADD PATH TO PATH LIST
path_frag_list[[length(path_frag_list) + 1]] <- c(0, path_vec, 0)
}
}
}
paths <- path_frag_list
# CONVERT PATHS TO STRINGS
paths_str <- unlist(lapply(paths, 'paste', collapse='-'))
for(i in 1:length(paths)){
# REMOVE PATHS WITH NA VALUE
#if(sum(is.na(paths[[i]])) > 0 && !is_open[i]){paths_str[i] <- NA; next}
# GET END JOINT
end_joint <- tail(paths[[i]], 1)
# REMOVE PATHS THAT END IN NON-FIXED JOINT THAT IS CONNECTED TO TWO OR MORE OTHER JOINTS (FALSE OPEN CHAIN)
if(end_joint > 0){
# SKIP IF JOINT IS "SOLE JOINT" - JOINT CONNECTED TO OTHERWISE ISOLATED BODY
if(end_joint %in% sole.joints) next
# FIND CONNECTED JOINTS
joints_conn_end <- unique(c(joint.conn[rowSums(end_joint == joint.conn[, 2:3]) > 0, 2:3]))
# REMOVE FOCAL JOINT AND ZERO
joints_conn_end <- joints_conn_end[!joints_conn_end %in% c(0, end_joint)]
# REMOVE FIXED JOINTS
joints_conn_end <- joints_conn_end[!joints_conn_end %in% fixed.joints]
# IF JOINTS REMAINING, MARK AS NA
if(length(joints_conn_end) > 1) paths_str[i] <- NA
# COERCE TO MATRIX
#if(is.vector(joints_conn_end)) joints_conn_end <- matrix(joints_conn_end, nrow=1, ncol=2)
#joints_conn_end <- joints_conn_end[rowSums(joints_conn_end == 0) == 0, ]
# IF MORE THAN ONE ROW (LENGTH > 2) MARK AS NA
#if(length(joints_conn_end) > 2) paths_str[i] <- NA
next
}
if(FALSE){
# REMOVE PATHS THAT DOUBLE BACK ON THE SAME LINK
bodies_in_path <- rep(NA, length(paths[[i]])-1)
for(j in 1:(length(paths[[i]])-1)){
# FIND BODY ASSOCIATED WITH PAIR OF JOINTS
body_num <- joint.conn[rowSums((joint.conn[, 2:3] == paths[[i]][j])+(joint.conn[, 2:3] == paths[[i]][j+1])) == 2, 1]
# PATH WITH ZERO AT ENDS TO INDICATE CLOSED PATH BUT ACTUALLY A FRAGMENT WITHIN CLOSED PATH
if(length(body_num) == 0) next
# SKIP IF 0
if(body_num == 1) next
# IF SAME BODY IS PRESENT IN PATH TWICE, MARK AS NA
if(body_num %in% bodies_in_path){
paths_str[i] <- NA
next
}
# ADD BODY NUMBER TO VECTOR
bodies_in_path[j] <- body_num
}
}
# REMOVE PATHS THAT ARE REVERSE OF ANOTHER PATH - EVERY FIXED-TO-FIXED PATH SHOULD HAVE REVERSE
#if(sum(paste(rev(paths[[i]]), collapse='-') == paths_str[-i], na.rm=TRUE) > 0) paths_str[i] <- NA
}
# REMOVE NA VALUES
paths_str <- paths_str[!is.na(paths_str)]
# SORT INTO CLOSED AND OPEN PATHS
paths_closed_str <- paths_str[grepl('^0-', paths_str) * grepl('-0$', paths_str) == 1]
paths_open_str <- paths_str[!grepl('-0$', paths_str)]
# REMOVE FIRST AND LAST ZEROES
paths_closed_str <- gsub('(^0-)|(-0$)', '', paths_closed_str)
paths_open_str <- gsub('^0-', '', paths_open_str)
# EXPLODE BACK INTO VECTOR
paths_closed <- lapply(strsplit(paths_closed_str, '-'), 'as.numeric')
paths_open <- lapply(strsplit(paths_open_str, '-'), 'as.numeric')
# SET ZERO-LENGTH PATHS AS NULL
if(length(paths_closed) == 0) paths_closed <- NULL
if(length(paths_open) == 0) paths_open <- NULL
list(
'paths.closed'=paths_closed,
'paths.open'=paths_open,
'fixed.joints'=fixed.joints,
'joint.conn'=joint.conn
)
}
aaronolsen/linkR documentation built on June 13, 2019, 5:39 p.m.
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findJointPaths <- function(body.conn, joint.types, solvable.paths, sole.joints){
# IF A SINGLE JOINT, RETURN 0,1
if(nrow(body.conn) == 1) return(list(
'paths.closed'=NULL,
'paths.open'=list(c(0,1)),
'fixed.joints'=1,
'joint.conn'=NULL
))
## CREATE MATRIX FOR CONNECTED JOINTS
joint.conn <- matrix(NA, nrow=0, ncol=3, dimnames=list(NULL, c('body.idx', 'joint1', 'joint2')))
# GET UNIQUE LINK INDICES
link_idx_unique <- sort(unique(c(body.conn)))
# NUMBER OF JOINTS
num_joints <- nrow(body.conn)
# FILL MATRIX OF CONNECTED JOINTS
for(link_idx in link_idx_unique){
# FIND ALL JOINTS CONNECTED TO LINK
joints_conn <- (1:num_joints)[(rowSums(link_idx == body.conn) == 1)]
# REMOVE NA VALUES
#joints_conn <- joints_conn[!is.na(joints_conn)]
# SKIP IF ONLY SINGLE JOINT CONNECTED
if(length(joints_conn) == 1) next
# GENERATE UNIQUE PAIRS
for(i in 1:(length(joints_conn)-1)){
for(j in (i+1):(length(joints_conn))){
joint.conn <- rbind(joint.conn, c(link_idx, sort(c(joints_conn[i], joints_conn[j]))))
}
}
}
# FIND JOINTS CONNECTED TO FIXED LINK (INCLUDES OPEN CHAIN WITH SINGLE JOINT CONNECTED TO FIXED LINK)
fixed.joints <- which(rowSums(body.conn == 1) > 0)
#fixed.joints <- unique(c(joint.conn[joint.conn[, 1] == 1, 2:3]))
# ADD ROWS FOR JOINTS CONNECTED TO THE FIXED LINK FOR EASIER PATH SEARCHING
joint.conn <- rbind(cbind(rep(1,length(fixed.joints)), rep(0,length(fixed.joints)), fixed.joints), joint.conn)
colnames(joint.conn) <- c('body.idx', 'joint1', 'joint2')
rownames(joint.conn) <- NULL
## FIND ALL JOINT PATHS
# INITIAL PATHS
paths <- list()
for(i in 1:length(fixed.joints)) paths[[i]] <- c(0, fixed.joints[i])
it <- 1
no_change <- FALSE
max_path_len <- 20
# FIND ALL UNIQUE FIXED TO FIXED PATHS
#while(it < 5){
while(no_change == FALSE){
#for(i in 1:length(paths)){cat('P');print(paths[[i]])}
no_change <- TRUE
for(i in 1:length(paths)){
#cat('P');print(paths[[i]])
# SKIP IF LAST JOINT IS NA
if(is.na(paths[[i]][length(paths[[i]])])) next
# SKIP IF LAST JOINT IS CONNECTED TO FIXED
if(paths[[i]][length(paths[[i]])] == 0) next
# SKIP IF PATH EXCEEDS MAXIMUM PATH LENGTH
if(length(paths[[i]]) > max_path_len) next
# GET LAST JOINT IN PATH
last_joint <- paths[[i]][length(paths[[i]])]
# FIND ALL CONNECTED JOINTS
joints_conn_idx <- rowSums(joint.conn[, 2:3] == last_joint) > 0
joints_conn <- unique(c(joint.conn[joints_conn_idx, 2:3]))
# REMOVE JOINTS ALREADY IN PATH EXCEPT ZEROS
joints_conn <- joints_conn[!joints_conn %in% paths[[i]][paths[[i]] > 0]]
# IF LAST JOINT IS JOINT CONNECTED TO FIXED LINK, REMOVE OTHER FIXED LINK JOINTS - AVOIDS LOOPS WITHIN FIXED LINK
if(last_joint %in% fixed.joints) joints_conn <- joints_conn[!joints_conn %in% fixed.joints]
# CHECK IF NO CONNECTED JOINTS
if(length(joints_conn) == 0) next
# REFINE TO LIMIT NUMBER OF LOOPS WITHIN LINK
if(TRUE){
if(length(paths[[i]]) > 1 && paths[[i]][length(paths[[i]])] != 0){
## IF LAST TWO JOINTS ARE WITHIN SAME BODY, REMOVE JOINTS IN THE SAME BODY - AVOIDS LOOPS WITHIN A LINK
# GET LAST TWO JOINTS
last_two <- paths[[i]][(length(paths[[i]])-1):length(paths[[i]])]
# FIND ASSOCIATED BODIES
body1 <- unique(body.conn[last_two[1], ])
body2 <- unique(body.conn[last_two[2], ])
# FIND SAME BODY BETWEEN TWO JOINTS
shared_body <- body1[body1 %in% body2]
# FIND JOINTS
if(length(shared_body) > 0){
# FIND JOINTS CONNECTED TO SHARED BODY
shared_body_joints <- unique(c(joint.conn[joint.conn[, 1] == shared_body, 2:3]))
# REMOVE
joints_conn <- joints_conn[!joints_conn %in% shared_body_joints]
}
# IF ALL CONNECTING JOINTS WERE ELIMINATED BECAUSE THEY WERE IN THE SAME LINK, ADD NA TO FLAG PATH FOR REMOVAL
if(length(joints_conn) == 0){
#paths[[i]] <- c(paths[[i]], NA)
next
}
}
#cat('J2 ');print(joints_conn)
}
# REMOVE ZERO IF PATH IS ONLY TWO JOINTS LONG
if(length(paths[[i]]) == 2) joints_conn <- joints_conn[joints_conn > 0]
# CHECK IF NO CONNECTED JOINTS
if(length(joints_conn) == 0) next
#cat('P');print(paths[[i]])
# SET CHANGE
no_change <- FALSE
# CREATE NEW PATHS IF MORE THAN ONE CONNECTING JOINT
if(length(joints_conn) > 1) for(j in 2:length(joints_conn)) paths[[length(paths)+1]] <- c(paths[[i]], joints_conn[j])
# ADD FIRST CONNECTING JOINT TO CURRENT PATH
paths[[i]] <- c(paths[[i]], joints_conn[1])
#cat('\n')
}
it <- it + 1
}
## BREAK UP CLOSED PATHS INTO FRAGMENTS
# FIND MINIMUM AND MAXIMUM FRAGMENT LENGTH TO SAVE
paths_nchar <- unlist(lapply(gsub('-', '', solvable.paths), 'nchar'))
frag_len_min <- min(paths_nchar)
frag_len_max <- max(paths_nchar)
# ADD REVERSE SOLVABLE PATHS
for(i in 1:length(solvable.paths)) solvable.paths <- c(solvable.paths, paste0(rev(strsplit(solvable.paths[i], '-')[[1]]), collapse='-'))
solvable.paths <- unique(solvable.paths)
# Remove paths with NA - may need to put this later?
#paths <- paths[unlist(lapply(lapply(paths, 'is.na'), 'sum')) == 0]
path_frags <- c()
path_frag_list <- list()
for(path_num in 1:length(paths)){
path <- paths[[path_num]]
# IF OPEN CHAIN SAVE BUT DO NOT BREAK INTO FRAGMENTS
if(path[1] == 0 && tail(path, 1) != 0){
path_frag_list[[length(path_frag_list) + 1]] <- path
next
}
for(frag_len in frag_len_min:min(length(path), frag_len_max)){
for(i in 1:(length(path)-frag_len+1)){
# SAVE PATH AS VECTOR
path_vec <- path[seq(i, i+frag_len-1)]
# REMOVE ZEROS
path_vec <- path_vec[path_vec != 0]
# CHECK IF FRAGMENT ALREADY EXISTS
if(paste(path_vec, collapse='-') %in% path_frags) next
#print(path_vec)
# CHECK IF FRAGMENT TYPE SEQUENCE IS SOLVABLE
if(!paste0(joint.types[path_vec], collapse='-') %in% solvable.paths) next
# MAKE SEQUENCE INTO STRING FOR EASY LOOK-UP
path_string <- paste(path_vec, collapse='-')
# ADD PATH TO VECTOR OF FRAGMENTS
path_frags <- c(path_frags, path_string)
# ADD PATH TO PATH LIST
path_frag_list[[length(path_frag_list) + 1]] <- c(0, path_vec, 0)
}
}
}
paths <- path_frag_list
# CONVERT PATHS TO STRINGS
paths_str <- unlist(lapply(paths, 'paste', collapse='-'))
for(i in 1:length(paths)){
# REMOVE PATHS WITH NA VALUE
#if(sum(is.na(paths[[i]])) > 0 && !is_open[i]){paths_str[i] <- NA; next}
# GET END JOINT
end_joint <- tail(paths[[i]], 1)
# REMOVE PATHS THAT END IN NON-FIXED JOINT THAT IS CONNECTED TO TWO OR MORE OTHER JOINTS (FALSE OPEN CHAIN)
if(end_joint > 0){
# SKIP IF JOINT IS "SOLE JOINT" - JOINT CONNECTED TO OTHERWISE ISOLATED BODY
if(end_joint %in% sole.joints) next
# FIND CONNECTED JOINTS
joints_conn_end <- unique(c(joint.conn[rowSums(end_joint == joint.conn[, 2:3]) > 0, 2:3]))
# REMOVE FOCAL JOINT AND ZERO
joints_conn_end <- joints_conn_end[!joints_conn_end %in% c(0, end_joint)]
# REMOVE FIXED JOINTS
joints_conn_end <- joints_conn_end[!joints_conn_end %in% fixed.joints]
# IF JOINTS REMAINING, MARK AS NA
if(length(joints_conn_end) > 1) paths_str[i] <- NA
# COERCE TO MATRIX
#if(is.vector(joints_conn_end)) joints_conn_end <- matrix(joints_conn_end, nrow=1, ncol=2)
#joints_conn_end <- joints_conn_end[rowSums(joints_conn_end == 0) == 0, ]
# IF MORE THAN ONE ROW (LENGTH > 2) MARK AS NA
#if(length(joints_conn_end) > 2) paths_str[i] <- NA
next
}
if(FALSE){
# REMOVE PATHS THAT DOUBLE BACK ON THE SAME LINK
bodies_in_path <- rep(NA, length(paths[[i]])-1)
for(j in 1:(length(paths[[i]])-1)){
# FIND BODY ASSOCIATED WITH PAIR OF JOINTS
body_num <- joint.conn[rowSums((joint.conn[, 2:3] == paths[[i]][j])+(joint.conn[, 2:3] == paths[[i]][j+1])) == 2, 1]
# PATH WITH ZERO AT ENDS TO INDICATE CLOSED PATH BUT ACTUALLY A FRAGMENT WITHIN CLOSED PATH
if(length(body_num) == 0) next
# SKIP IF 0
if(body_num == 1) next
# IF SAME BODY IS PRESENT IN PATH TWICE, MARK AS NA
if(body_num %in% bodies_in_path){
paths_str[i] <- NA
next
}
# ADD BODY NUMBER TO VECTOR
bodies_in_path[j] <- body_num
}
}
# REMOVE PATHS THAT ARE REVERSE OF ANOTHER PATH - EVERY FIXED-TO-FIXED PATH SHOULD HAVE REVERSE
#if(sum(paste(rev(paths[[i]]), collapse='-') == paths_str[-i], na.rm=TRUE) > 0) paths_str[i] <- NA
}
# REMOVE NA VALUES
paths_str <- paths_str[!is.na(paths_str)]
# SORT INTO CLOSED AND OPEN PATHS
paths_closed_str <- paths_str[grepl('^0-', paths_str) * grepl('-0$', paths_str) == 1]
paths_open_str <- paths_str[!grepl('-0$', paths_str)]
# REMOVE FIRST AND LAST ZEROES
paths_closed_str <- gsub('(^0-)|(-0$)', '', paths_closed_str)
paths_open_str <- gsub('^0-', '', paths_open_str)
# EXPLODE BACK INTO VECTOR
paths_closed <- lapply(strsplit(paths_closed_str, '-'), 'as.numeric')
paths_open <- lapply(strsplit(paths_open_str, '-'), 'as.numeric')
# SET ZERO-LENGTH PATHS AS NULL
if(length(paths_closed) == 0) paths_closed <- NULL
if(length(paths_open) == 0) paths_open <- NULL
list(
'paths.closed'=paths_closed,
'paths.open'=paths_open,
'fixed.joints'=fixed.joints,
'joint.conn'=joint.conn
)
}
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