diff --git a/src/ol/reproj/Triangulation.js b/src/ol/reproj/Triangulation.js
index 9fe7270abd..d5c7580584 100644
--- a/src/ol/reproj/Triangulation.js
+++ b/src/ol/reproj/Triangulation.js
@@ -247,12 +247,19 @@ class Triangulation {
     }
 
     if (!needsSubdivision && this.maxSourceExtent_) {
-      if (!intersects(sourceQuadExtent, this.maxSourceExtent_)) {
-        // whole quad outside source projection extent -> ignore
-        return;
+      if (isFinite(sourceQuadExtent[0]) &&
+          isFinite(sourceQuadExtent[1]) &&
+          isFinite(sourceQuadExtent[2]) &&
+          isFinite(sourceQuadExtent[3])) {
+          if (!intersects(sourceQuadExtent, this.maxSourceExtent_)) {
+            // whole quad outside source projection extent -> ignore
+            return;
+          }
       }
     }
 
+    let isNotFinite = 0;
+
     if (!needsSubdivision) {
       if (!isFinite(aSrc[0]) || !isFinite(aSrc[1]) ||
           !isFinite(bSrc[0]) || !isFinite(bSrc[1]) ||
@@ -261,7 +268,16 @@ class Triangulation {
         if (maxSubdivision > 0) {
           needsSubdivision = true;
         } else {
-          return;
+          // It might be the case that only 1 of the points is infinite. In this case
+          // we can draw a single triangle with the other three points
+          isNotFinite =
+              (((!isFinite(aSrc[0]) || !isFinite(aSrc[1])) | 0) << 3) +
+              (((!isFinite(bSrc[0]) || !isFinite(bSrc[1])) | 0) << 2) +
+              (((!isFinite(cSrc[0]) || !isFinite(cSrc[1])) | 0) << 1) +
+               ((!isFinite(dSrc[0]) || !isFinite(dSrc[1])) | 0);
+          if (isNotFinite != 1 && isNotFinite != 2 && isNotFinite != 4 && isNotFinite != 8) {
+            return;
+          }
         }
       }
     }
@@ -320,8 +336,22 @@ class Triangulation {
       this.wrapsXInSource_ = true;
     }
 
-    this.addTriangle_(a, c, d, aSrc, cSrc, dSrc);
-    this.addTriangle_(a, c, b, aSrc, cSrc, bSrc);
+    // Exactly zero or one of *Src is not finite
+    if ((isNotFinite & 0xb) == 0) {
+      this.addTriangle_(a, c, d, aSrc, cSrc, dSrc);
+    }
+    if ((isNotFinite & 0xe) == 0) {
+      this.addTriangle_(a, c, b, aSrc, cSrc, bSrc);
+    }
+    if (isNotFinite) {
+      // Try the other two triangles
+      if ((isNotFinite & 0xd) == 0) {
+        this.addTriangle_(b, d, a, bSrc, dSrc, aSrc);
+      }
+      if ((isNotFinite & 0x7) == 0) {
+        this.addTriangle_(b, d, c, bSrc, dSrc, cSrc);
+      }
+    }
   }
 
   /**