diff --git a/crates/geom/src/homography.rs b/crates/geom/src/homography.rs
index b27ecef2..daa11b05 100644
--- a/crates/geom/src/homography.rs
+++ b/crates/geom/src/homography.rs
@@ -51,11 +51,11 @@ impl Homography {
         let c01 = m[5] * m[6] - m[3] * m[8];
         let c02 = m[3] * m[7] - m[4] * m[6];
         let det = m[0] * c00 + m[1] * c01 + m[2] * c02;
-        if det.abs() < 1e-300 {
+        if !det.is_finite() || det.abs() < 1e-300 {
             return None;
         }
         let inv = 1.0 / det;
-        Some(Homography([
+        let coefficients = [
             c00 * inv,
             (m[2] * m[7] - m[1] * m[8]) * inv,
             (m[1] * m[5] - m[2] * m[4]) * inv,
@@ -65,11 +65,17 @@ impl Homography {
             c02 * inv,
             (m[1] * m[6] - m[0] * m[7]) * inv,
             (m[0] * m[4] - m[1] * m[3]) * inv,
-        ]))
+        ];
+        coefficients.iter().all(|v| v.is_finite()).then_some(Homography(coefficients))
     }
 
     /// The homography mapping `src[i]` → `dst[i]` (4 correspondences, DLT with h33 = 1).
     pub fn from_quads(src: &[Point; 4], dst: &[Point; 4]) -> Option<Homography> {
+        // Failed feature matches and invalid perspective parameters can contain
+        // non-finite coordinates. Do not return a transform that poisons rendering.
+        if src.iter().chain(dst.iter()).any(|p| !p.x.is_finite() || !p.y.is_finite()) {
+            return None;
+        }
         let mut a = [[0.0f64; 9]; 8];
         for i in 0..4 {
             let (x, y) = (src[i].x, src[i].y);
@@ -80,7 +86,7 @@ impl Homography {
         // Gaussian elimination with partial pivoting on the 8×8 system (last column = rhs).
         for col in 0..8 {
             let piv = (col..8).max_by(|&i, &j| a[i][col].abs().total_cmp(&a[j][col].abs()))?;
-            if a[piv][col].abs() < 1e-12 {
+            if !a[piv][col].is_finite() || a[piv][col].abs() < 1e-12 {
                 return None;
             }
             a.swap(col, piv);
@@ -94,7 +100,7 @@ impl Homography {
             }
         }
         let h: Vec<f64> = (0..8).map(|i| a[i][8] / a[i][i]).collect();
-        Some(Homography([h[0], h[1], h[2], h[3], h[4], h[5], h[6], h[7], 1.0]))
+        h.iter().all(|v| v.is_finite()).then_some(Homography([h[0], h[1], h[2], h[3], h[4], h[5], h[6], h[7], 1.0]))
     }
 }
 
@@ -121,4 +127,19 @@ mod tests {
         let src = [Point::new(0.0, 0.0); 4];
         assert!(Homography::from_quads(&src, &src).is_none());
     }
+
+    #[test]
+    fn nonfinite_projective_and_affine_transforms_are_rejected() {
+        let src = [Point::new(0.0, 0.0), Point::new(1.0, 0.0), Point::new(1.0, 1.0), Point::new(0.0, 1.0)];
+        let mut invalid = src;
+        invalid[2].x = f64::NAN;
+        assert!(Homography::from_quads(&invalid, &src).is_none());
+        invalid[2].x = f64::INFINITY;
+        assert!(Homography::from_quads(&src, &invalid).is_none());
+        assert!(Homography([f64::NAN, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0]).inverse().is_none());
+        assert!(Homography([f64::INFINITY, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0]).inverse().is_none());
+        assert!(Affine([f64::NAN, 0.0, 0.0, 1.0, 0.0, 0.0]).inverse().is_none());
+        assert!(Affine([f64::INFINITY, 0.0, 0.0, 1.0, 0.0, 0.0]).inverse().is_none());
+        assert_eq!(Affine::IDENTITY.inverse(), Some(Affine::IDENTITY));
+    }
 }
diff --git a/crates/geom/src/lib.rs b/crates/geom/src/lib.rs
index 1d81279d..4b8f623e 100644
--- a/crates/geom/src/lib.rs
+++ b/crates/geom/src/lib.rs
@@ -234,12 +234,13 @@ impl Affine {
     }
     pub fn inverse(&self) -> Option<Affine> {
         let det = self.determinant();
-        if det.abs() < 1e-300 {
+        if !det.is_finite() || det.abs() < 1e-300 {
             return None;
         }
         let [a, b, c, d, e, f] = self.0;
         let inv = 1.0 / det;
-        Some(Affine([d * inv, -b * inv, -c * inv, a * inv, (c * f - d * e) * inv, (b * e - a * f) * inv]))
+        let coefficients = [d * inv, -b * inv, -c * inv, a * inv, (c * f - d * e) * inv, (b * e - a * f) * inv];
+        coefficients.iter().all(|v| v.is_finite()).then_some(Affine(coefficients))
     }
     /// Bounding box of a transformed rectangle.
     pub fn transform_rect_bbox(&self, r: &Rect) -> Rect {