To prepare cake, place sugar and oil in a large bowl; beat with a mixer at high speed for 2 minutes or until well blended. Add eggs, 1 at a time, beating well after each addition. Add rinds, vanilla, and yogurt; beat until combined.
Weigh or lightly spoon flour and cornmeal into dry measuring cups; level with a knife. Combine flour, cornmeal, baking soda, baking powder, and salt, stirring with a whisk. Add flour mixture to oil mixture; stir with a whisk just until combined. Pour batter into a 9-inch springform pan coated with cooking spray. Bake at 325° for 30 minutes or until golden brown and a wooden pick inserted in center comes out clean. Cool 10 minutes on a wire rack; remove sides from pan. Cool cake completely on rack.
To prepare compote, peel and section grapefruit and oranges over a medium bowl, reserving juices; place sections in another bowl. Combine reserved juices and lime juice in a small saucepan; bring to a boil. Stir in honey and allspice; reduce heat, and simmer 4 minutes or until syrupy. Cover and chill 30 minutes. Pour over fruit sections; toss gently. Chill. Serve compote over cake.