構図, 構想, and 発想: composition, planning, and a new way of thinking
Compare 構図 in photographs and sketches, 構想 for a library or novel, and 発想 behind a game or the reuse of boxes.
構図: placing a person and refining a sketch’s composition
「人物を中央に置く構図で写真を撮った。」 means “I took the photograph with the person in the center of the composition.” 構図（こうず） means composition or layout. 人物を中央に置く is the placement of the person within the photograph, not a general claim about the person’s character or everyday location.
「画家は下絵を描きながら全体の構図を整えた。」 means “The painter refined the overall composition while sketching.” 下絵を描きながら means while sketching. The painter refined the overall composition during that activity; this refinement alone does not establish that the final painting was completed.
構想: a library concept in a drawing and a long-developed novel plan
「新しい図書館の構想を図にまとめた。」 means “I organized the concept for the new library in a drawing.” 構想（こうそう） means a concept or plan. 図にまとめた describes organizing the library concept in a drawing, keeping the representation of a plan distinct from a constructed building.
「長年温めてきた小説の構想を語った。」 means “I discussed the plan for a novel that I had been developing for a long time.” 長年温めてきた describes developing the novel’s plan over a long period. 語った is the action of discussing that plan, without establishing that the novel itself was completed at that point.
発想: a game from imagination and a new use for boxes
「子どもの自由な発想から面白い遊びが生まれた。」 means “A fun game grew out of the child's free imagination.” 発想（はっそう） means an idea or way of thinking. The child’s free imagination gave rise to a fun game, showing a relationship between an idea and the game it inspired.
「発想を変えて余った箱を収納に使った。」 means “I changed my way of thinking and used the leftover boxes for storage.” 発想を変えて describes changing a way of thinking and using the leftover boxes for storage. Its object and role differ from refining a picture’s 構図 or discussing a novel’s 構想.
Does 新しい図書館の構想を図にまとめた mean that the library was completely built?
Show the answer and why
No. The library concept was organized in a drawing. 構想 is the plan, 構図 concerns placement within an image, and 発想 concerns an idea or way of thinking, such as finding a storage use for boxes.