lambdaway :: line_intersection

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_h1 line intersection

_p Following [[rosettacode|https://rosettacode.org/wiki/Find_the_intersection_of_two_lines]] Find the point of intersection of two lines in 2D:

_ul The 1st line passes though   (4,0)   and   (6,10) .
_ul The 2nd line passes though   (0,3)   and   (10,7) .

{pre
'{def line_intersect
 {def line_intersect.sub
  {lambda {:111 :121 :112 :122 :211 :221 :212 :222}
   {let { {:x :111}
          {:y :121} 
          {:z {- {* {- :222 :221}
                    {- :112 :111}}
                 {* {- :212 :211}
                    {- :122 :121}} } }
          {:f {- :111 :211}}
          {:a {- :112 :111}}
          {:g {- :121 :211}}
          {:e {- :121 :221}}
          {:b {- :122 :121}}
          {:c {- :212 :211}}
          {:d {- :222 :221}}
        } {if {> :z 0}
           then {A.new ∞
                       ∞}
           else {let { {:x :x} 
                       {:y :y}
                       {:a :a}
                       {:b :b}
                       {:t1 {/ {- {* :c :e}
                                  {* :d :f}}
                               :z} }
                       {:t2 {/ {- {* :a :g}
                                  {* :b :f}}
                               :z} }
                } {if {and {>= :t1 0}
                           {<= :t1 1}
                           {>= :t2 0}
                           {<= :t2 1}}
                   then {A.new {+ :x
                                  {* :t1 :a}}
                               {+ :y
                                  {* :t1 :b}} }
                   else {A.new ∞
                               ∞}} }}}}}
 {lambda {:1 :2}
  {line_intersect.sub 
   {A.first {A.first :1}}
   {A.last  {A.first :1}}     ;; :111 :121
   {A.first {A.last  :1}}
   {A.last  {A.last  :1}}     ;; :112 :122
   {A.first {A.first :2}} 
   {A.last  {A.first :2}}     ;; :211 :221
   {A.first {A.last  :2}}
   {A.last  {A.last  :2}} }}} ;; :212 :222
-> {def line_intersect
 {def line_intersect.sub
  {lambda {:111 :121 :112 :122 :211 :221 :212 :222}
   {let { {:x :111} {:y :121} 
          {:z {- {* {- :222 :221} {- :112 :111}}
                 {* {- :212 :211} {- :122 :121}} } }
          {:a {- :112 :111}} {:b {- :122 :121}}
          {:c {- :212 :211}} {:d {- :222 :221}}
          {:e {- :121 :221}} {:f {- :111 :211}}
          {:g {- :121 :211}} {:h {- :122 :121}}
        } {if {> :z 0}
           then {A.new ∞ ∞}
           else {let { {:x :x} {:y :y} {:a :a} {:b :b}
                       {:t1 {/ {- {* :c :e} {* :d :f}} :z} }
                       {:t2 {/ {- {* :a :g} {* :b :f}} :z} }
                } {if {and {>= :t1 0} {<= :t1 1} {>= :t2 0} {<= :t2 1}}
                   then {A.new {+ :x {* :t1 :a}} {+ :y {* :t1 :b}} }
                   else {A.new ∞ ∞}} }}}}}
 {lambda {:1 :2}
  {line_intersect.sub 
   {A.first {A.first :1}} {A.last {A.first :1}}     ;; :111 :121
   {A.first {A.last  :1}} {A.last {A.last  :1}}     ;; :112 :122
   {A.first {A.first :2}} {A.last {A.first :2}}     ;; :211 :221
   {A.first {A.last  :2}} {A.last {A.last  :2}} }}} ;; :212 :222

'{line_intersect {A.new {A.new 4 0} {A.new 6 10}}
                {A.new {A.new 0 3} {A.new 10 7}}}
-> {line_intersect {A.new {A.new 4 0} {A.new 6 10}}
                {A.new {A.new 0 3} {A.new 10 7}}}
'{line_intersect {A.new {A.new 4 0} {A.new 6 10}}
                {A.new {A.new 0 3} {A.new 10 7.1}}}
-> {line_intersect {A.new {A.new 4 0} {A.new 6 10}}
                {A.new {A.new 0 3} {A.new 10 7.1}}}
'{line_intersect {A.new {A.new 1 -1} {A.new 4 4}}
                {A.new {A.new 2 5} {A.new 3 -2}}}
-> {line_intersect {A.new {A.new 1 -1} {A.new 4 4}}
                {A.new {A.new 2 5} {A.new 3 -2}}}
'{line_intersect {A.new {A.new 0 0} {A.new 0 0}}
                {A.new {A.new 0 3} {A.new 10 7}}}
-> {line_intersect {A.new {A.new 0 0} {A.new 0 0}}
                {A.new {A.new 0 3} {A.new 10 7}}}
'{line_intersect {A.new {A.new 0 0} {A.new 1 1}}
                {A.new {A.new 1 2} {A.new 4 5}}}
-> {line_intersect {A.new {A.new 0 0} {A.new 1 1}}
                {A.new {A.new 1 2} {A.new 4 5}}}

}