The law is an ass.
We have a constitution and under that document I get to live and survive. If Lane County has thousands of homeless and there is no public shelter system for them, then they get to live where they can, and if that means finding a place in a park or by the river, then such is life.
If someone would finally bring a case to the Supreme Court under the "no bed, no arrest" principle, and if the Supreme Court would rule that the constitution protects homeless people, Lane County would have to find a place for homeless people to "camp", and there would be no question as to NIMBY or local ordinance. I have absolutely no doubt that, under court order, Lane County and Eugene would find enough housing for all the homeless, in a heartbeat. As it is, caring people have to beg to help. 
Then, if there were a public shelter system, the authorities could cite and arrest people for living rough, as it isn't healthy for them or the community, but only then.
Hugh Massengill, Eugene