added tests, but one fails refs idaholab#21903

test/tests/meshgenerators/transfinite_generator/arccircle_generator.i

@@ -0,0 +1,21 @@
+[Mesh]
+  [transf]
+    type = TransfiniteMeshGenerator
+    corners = '-1.0 -1.0 0.0
+              10.0 -1.0 0.0
+              11.0 5.0 0
+              4.0 4.0 0'
+    nx = 8 
+    ny = 6 
+    bottom = LINE
+    top = LINE
+    right = CIRCARC
+    left = LINE
+    right_parameter = '1.23'              
+  []
+[]
+
+[Outputs]
+  exodus = true
+  xda = true
+[]

test/tests/meshgenerators/transfinite_generator/quadrilater_generator.i

@@ -0,0 +1,20 @@
+[Mesh]
+  [transf]
+    type = TransfiniteMeshGenerator
+    corners = '-1.0 -1.0 0.0
+              10.0 -1.0 0.0
+              11.0 5.0 0
+              4.0 4.0 0'
+    nx = 8 
+    ny = 6 
+    bottom = LINE
+    top = LINE
+    right = LINE
+    left = LINE              
+  []
+[]
+
+[Outputs]
+  exodus = true
+  xda = true
+[]

test/tests/meshgenerators/transfinite_generator/tests

@@ -0,0 +1,30 @@
+[Tests]
+  issues = '#21903'
+  design = 'meshgenerators/TransfiniteGenerator.md'
+
+  [generate]
+    requirement = 'The system shall support the ability to create a mesh element-wise by specifying '
+                  'corners, edge types, generating parameters and/or point distribution, '	
+
+    [quadrilater]
+      type = 'Exodiff'
+      input = 'quadrilater_generator.i'
+      cli_args = '--mesh-only'
+      exodiff = 'quadrilater_generator_in.e'
+      recover = false
+
+      detail = 'resulting in a quadrilateral mesh, or'
+
+    []
+
+    [arccircle]
+      type = 'Exodiff'
+      input = 'arccircle_generator.i'
+      cli_args = '--mesh-only'
+      exodiff = arccircle_generator_in.e'
+      recover = false
+
+      detail = 'resulting in a mesh with one arc circle side.'
+    []
+  []
+[]