In　order　to　study　the　theory　and　application　of　computer　aided　design　(CAD)　related　to　the　composition　of　art,　the　theory　of　symbolic　matrix　was　introduced　to　realize　the　purpose　of　the　study　of　the　interaction　between　perceptual　and　rational　problems.　In　this　paper,　the　original　image　was　extracted　from　the　design　object,　and　the　transformation　between　the　original　image　and　the　symbol　matrix　was　realized　by　the　correspondence　with　the　elements　in　the　matrix.　Based　on　the　research　route,　four　kinds　of　mathematical　models　were　established,　namely　random　distribution,　symmetric　distribution,　central　diffusion,　and　reorganization.　By　applying　the　mathematical　model　constructed　in　this　paper,　the　picture　was　transformed,　the　combination　of　various　styles　of　graphics　was　added,　and　how　to　put　the　simple　image　picture　into　a　meaningful　integrated　image　picture　was　discussed.　The　computer-aided　design　method　of　the　existing　verification　examples　was　summarized　in　this　paper,　and　the　design　method　was　accurate　and　effective.　Compared　with　traditional　graphic　art　design　methods,　the　computer-aided　design　method　mentioned　in　the　paper　has　the　following　advantages.　Computer-aided　design　can　quickly　process　and　analyze　images,　convert　and　combine　them　through　mathematical　models　and　algorithms,　greatly　saving　designers　time　and　energy.　By　introducing　symbol　matrix　theory　and　establishing　various　mathematical　models,　computer-aided　design　can　provide　diverse　graphic　combinations　and　style　transformations,　helping　designers　explore　more　innovative　design　solutions.　©　2025　World　Scientific　Publishing　Company.