Non-overlapping rectangles constrained to a boundary

I am trying to model placement of parts on a circuit board. Without anymeaningful constraints, my basic schema looks like this:

create table part (    part_id bigserial primary key,    name text not null,    width double precision not null,    height double precision not null);create table board (    board_id bigserial primary key,    width double precision not null,    height double precision not null);create table board_part (    board_id bigint not null references board,    part_id bigint not null references part,    position point not null);

^{(SQL Fiddle, Visualization)}

For b and b2 any board_parts, I want to enforce the followingconstraints:

1. b lies on the board:

   box(b.position, point(b.part.width,b.part.height))<@ box(point(0,0), point(b.board.width,b.board.height))

2. b and b2 do not overlap if they lie on the same board:

   b.board_id != b2.board_id ornot (box(b.position, point(b.part.width,b.part.height))&& box(b2.position, point(b2.part.width,b2.part.height)))

How can I achieve this (without too much data duplication)? Changing the schema is fine.

Here is my best attempt (SQL Fiddle), takinginspiration fromErwin's answer to my previous question.It enforces the constraints I wanted, but has a lot of duplicate data in the board_part table. I imagine I could write a function to fill in the board_width, board_height, part_width, and part_height fields automatically, but it still feels wrong having so much duplicate data around. Also, keying to the width/height fields feels like a hack.