限制在边界上的不重叠矩形

Question

我正在尝试对电路板上零件的放置进行建模。没有任何有意义的限制，我的基本架构如下所示：

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，可视化）}

对于b和b2any board_parts，我想强制执行以下约束：

1. b位于黑板上：

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

2. bb2如果它们位于同一块板上，则不会重叠：

   b.board_id != b2.board_id or
   not (box(b.position, point(b.part.width,b.part.height))
           && box(b2.position, point(b2.part.width,b2.part.height)))
   

我怎样才能实现这一点（没有太多的数据重复）？改变架构就好了。

这是我的最佳尝试（SQL Fiddle），从埃尔文对我之前问题的回答中汲取灵感。它强制执行我想要的约束，但表中有很多重复数据board_part。我想我可以编写一个函数来自动填充board_width、board_height、part_width和part_height字段，但周围有这么多重复数据仍然感觉不对。另外，键入width/height字段感觉就像黑客。

Answer 1

基本答案

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我建议使用几何类型box和排除约束（Postgres 9.2+）。应该是完美的解决您的问题。它隐式创建一个也支持某些查询的 GiST 索引。

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将其与 equal on 结合起来board_id以允许在一个表中包含多个板。您将需要附加模块btree_gist。每个数据库一次：

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CREATE EXTENSION btree_gist;\n

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要将零件限制在板上，请添加CHECK约束。您需要板子的限制盒board_part（冗余）。可能看起来像这样：

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CREATE TABLE board_part (\n  board_id bigint NOT NULL REFERENCES board\n, board_box box NOT NULL\n, part_id bigint NOT NULL REFERENCES part\n, part_box box NOT NULL\n, EXCLUDE USING gist (board_id WITH =, part_box WITH &&)\n, CHECK (part_box <@ board_box)\n);\n

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&&..“重叠”运算符
\n<@ ..“包含”运算符

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缺点：您需要表中每个零件和盒子的尺寸board_part多余的每个零件和盒子的尺寸。

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高级答案

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为了避免冗余存储，我更喜欢这个新想法：FakeIMMUTABLE函数返回 id 的框并在这些函数上构建约束。您的表格只需使用原始设计的列即可。

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我进行了完整的测试来验证它是否有效。

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完整架构

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基表：

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CREATE TABLE part (\n  part_id serial PRIMARY KEY\n, part text NOT NULL\n, wide int NOT NULL\n, high int NOT NULL\n);\n\nCREATE TABLE board (\n  board_id serial PRIMARY KEY\n, board text NOT NULL\n, wide int NOT NULL\n, high int NOT NULL\n);\n

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IMMUTABLE功能：

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CREATE OR REPLACE FUNCTION f_boardbox(_board_id int)\n  RETURNS box\n  LANGUAGE sql IMMUTABLE AS\n\'SELECT box(point(0,0), point (b.wide, b.high))\n FROM   public.board b WHERE board_id = $1\'; \n\nCREATE OR REPLACE FUNCTION f_partbox(_part_id int, _wide int, _high int)\n  RETURNS box\n  LANGUAGE sql IMMUTABLE AS\n\'SELECT box(point($2,$3), point($2 + p.wide, $3 + p.high))\n FROM   public.part p WHERE part_id = $1\';\n

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替换public为表的实际架构。
\n在 Postgres 9.6 或更高版本中添加PARALLEL SAFE. 看：

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• 何时将函数标记为 PARALLEL RESTRICTED 与 PARALLEL SAFE？
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主表：

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CREATE TABLE board_part (\n  board_id int NOT NULL REFERENCES board\n, part_id int NOT NULL REFERENCES part\n, wide int NOT NULL\n, high int NOT NULL\n, EXCLUDE USING gist (board_id WITH =, f_partbox(part_id, wide, high) WITH &&)\n, CHECK (f_partbox(part_id, wide, high) <@ f_boardbox(board_id))\n);\n

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当然，如果您更新 aboard_id或part_id正在使用的维度，则部分索引和/或约束无效。您需要重新创建任何索引或约束，其基础是以下承诺：IMMUTABLE函数返回值永不改变的承诺的任何索引或约束。看：

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• PostgreSQL 是否支持 \xe2\x80\x9caccent insensitive\xe2\x80\x9d 排序规则？
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但是，您可以使用触发器来避免这种昂贵的操作，以仅更新受影响的行：

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触发器

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CREATE OR REPLACE FUNCTION f_board_upaft()\n  RETURNS trigger\n  LANGUAGE plpgsql AS\n$func$\nBEGIN\n   UPDATE board_part\n   SET    board_id = board_id        -- enough to trigger CHECK constraint\n   WHERE  board_id = NEW.board_id;   -- limit to relevant rows\n\n   RETURN NULL;\nEND\n$func$;\n\nCREATE TRIGGER board_upaft\nAFTER UPDATE OF wide, high ON board  -- limit to relevant columns\nFOR EACH ROW EXECUTE PROCEDURE f_board_upaft();\n\n\nCREATE OR REPLACE FUNCTION f_part_upaft()\n  RETURNS trigger\n  LANGUAGE plpgsql AS\n$func$\nBEGIN\n   UPDATE board_part\n   SET    part_id = 0\n   WHERE  part_id = NEW.part_id;\n\n   UPDATE board_part\n   SET    part_id = NEW.part_id\n   WHERE  part_id = 0;               -- enough to update EXCL. constraint\n\n   RETURN NULL;\nEND\n$func$;\n\nCREATE TRIGGER part_upaft\nAFTER UPDATE OF wide, high ON part\nFOR EACH ROW EXECUTE PROCEDURE f_part_upaft();\n

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part_id = 0是表中的特殊行part。触发器需要。

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测试数据：

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INSERT INTO board (board, wide, high)\nVALUES (\'b1010\',10,10), (\'b2030\',20, 30);\n\nINSERT INTO part (part_id, part, wide, high)\nVALUES (0,\'p0\',0,0);          -- special row needed for trigger!\n\nINSERT INTO part (part, wide, high)\nVALUES (\'p11\',1,1), (\'p33\',3,3);\n\nINSERT INTO board_part (board_id, part_id, wide, high)\nVALUES (1,1,3,3)\n     , (1,1,5,5)   -- no overlap, inside board\n     , (2,1,3,3);  -- different board, no overlap\n

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测试

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如果触发器和约束完成其工作，这些必须引发异常：

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UPDATE part SET wide = 6 , high = 6\nWHERE  part_id = 1;            -- violates EXCL. & CHECK constraint\n\nUPDATE part SET wide = 3 , high = 3\nWHERE  part_id = 1;            -- violates EXCL. constraint\n\nUPDATE board SET wide = 2 , high = 2\nWHERE  board_id = 1;            -- violates CHECK constraint\n

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db<>在这里小提琴
\n_{旧的sqlfiddle}

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